Illustrative Math Alignment: Grade 7 Unit 7
Expressions, Equations, and Inequalities
Lesson 4: Reasoning about Equations and Tape Diagrams (Part 1)
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 10 | Solving Equations with Angle Measures 2--Example 10TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 2 | Solving Equations with Angle Measures 2--Example 2TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 3 | Solving Equations with Angle Measures 2--Example 3TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 4 | Solving Equations with Angle Measures 2--Example 4TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 5 | Solving Equations with Angle Measures 2--Example 5TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 6 | Solving Equations with Angle Measures 2--Example 6TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 7 | Solving Equations with Angle Measures 2--Example 7TopicEquations DescriptionThis example demonstrates solving equations involving angle measures in a kite. A kite has two pairs of adjacent congruent angles. In this case, we have angles represented as (x+50)°, (x+50)°, (y+20)°, and y°. To solve this problem, we apply two key principles: the sum of angles in a quadrilateral is 360°, and the sum of the angles of a triangle is 180°. You can use the triangle equation to solve for y. Once you determine the value for y, you can use that to find x using either the triangle or the quadrilateral equation. In the solution shown, the triangle equation is used. |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 8 | Solving Equations with Angle Measures 2--Example 8TopicEquations DescriptionThis example illustrates solving equations involving angle measures in a kite. The kite has two known angles of 70° and 40°, and two unknown angles represented as (x+y)°. To solve this problem, we look at the triangles formed by one of the diagonals of the kite and use the triangle equation. First solve for x with the top triangle. Once you find x, use that value to solve for y in the bottom triangle. You could also use the quadrilateral equation to solve for y. |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 9 | Solving Equations with Angle Measures 2--Example 9TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 1 | Solving Equations with Angle Measures--Example 1TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 10 | Solving Equations with Angle Measures--Example 10TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 11 | Solving Equations with Angle Measures--Example 11TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 12 | Solving Equations with Angle Measures--Example 12TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 13 | Solving Equations with Angle Measures--Example 13TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 14 | Solving Equations with Angle Measures--Example 14TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 15 | Solving Equations with Angle Measures--Example 15TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 2 | Solving Equations with Angle Measures--Example 2TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 3 | Solving Equations with Angle Measures--Example 3TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 4 | Solving Equations with Angle Measures--Example 4TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 5 | Solving Equations with Angle Measures--Example 5TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 6 | Solving Equations with Angle Measures--Example 6TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 7 | Solving Equations with Angle Measures--Example 7TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 8 | Solving Equations with Angle Measures--Example 8TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 9 | Solving Equations with Angle Measures--Example 9TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 1 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 1TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition demonstrates solving the equation 2x + 3 = 7 by performing two inverse operations to isolate x. The operations shown are subtracting 3 from both sides and then dividing by 2. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 10 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 10TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition involves solving -3x + (-12) = -42 by performing two inverse operations: addition and division to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 2 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 2TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition shows solving the equation 3x + 4 = 13 by using two inverse operations. The steps involve subtracting 4 and then dividing by 3. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 3 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 3TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition involves solving the equation 2x + 4 = 8 using inverse operations. It shows subtraction and division to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 4 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 4TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition illustrates solving -4x + 5 = 25. It uses inverse operations by subtracting 5 and dividing by -4. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 5 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 5TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition shows the solution to -7x + 6 = 48 by isolating x with inverse operations, including subtraction and division. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 6 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 6TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition solves the equation 6x + (-2) = 34 by using inverse operations, specifically addition and division, to find the value of x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 7 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 7TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition solves 10x + (-6) = 54 by isolating x through inverse operations, including addition and division. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 8 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 8TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition shows solving -x + (-5) = 71 by performing inverse operations to isolate x, using addition and division by -1. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 9 | Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 9TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and addition demonstrates solving -2x + (-8) = 22 through inverse operations, specifically addition and division, to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 1 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 1TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction shows solving the equation 2x - 3 = 7 by isolating x through inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 10 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 10TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction demonstrates solving the equation -3x - (-12) = -42 by isolating x through inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 2 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 2TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction illustrates solving the equation 3x - 4 = 14 by isolating x with inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 3 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 3TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction demonstrates solving the equation -2x - 4 = 8 by isolating x using inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 4 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 4TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction explains solving the equation -x - 5 = 17 by isolating x with inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 5 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 5TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction shows solving the equation -7x - 6 = 43 by isolating x with inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 6 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 6TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction illustrates solving the equation 6x - (-2) = 38 by isolating x using inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 7 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 7TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction demonstrates solving the equation 10x - (-6) = 76 by isolating x through inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 8 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 8TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction explains solving the equation -x - (-5) = 71 by isolating x through inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 9 | Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 9TopicSolving Equations DescriptionAn example of solving a two-step equation involving multiplication and subtraction shows solving the equation -2x - (-8) = 22 by isolating x with inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 1 | Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 1TopicSolving Equations DescriptionAn example of solving a two-step equation with division and addition: x/5 + 3 = 7. The solution is detailed with inverse operations to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 10 | Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 10TopicSolving Equations DescriptionAn example of solving a two-step equation with division and addition: -x/3 + (-12) = -42. The solution follows each step using inverse operations to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 2 | Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 2TopicSolving Equations DescriptionAn example of solving a two-step equation with division and addition: x/4 + 4 = 14. It includes each step to isolate the variable using inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 3 | Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 3TopicSolving Equations DescriptionAn example of solving a two-step equation with division and addition: -x/3 + 4 = 8. The solution uses inverse operations to isolate x with careful handling of the negative sign. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 4 | Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 4TopicSolving Equations DescriptionAn example of solving a two-step equation with division and addition: -x/6 + 5 = 17. The solution details each inverse operation step to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 5 | Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 5TopicSolving Equations DescriptionAn example of solving a two-step equation with division and addition: -x/7 + 6 = 43. The solution carefully applies inverse operations to solve for x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations. |
Solving Two-Step Equations |
