Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 8: Reasoning about Solving Equations (Part 2)

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example--Solving Equations--Equations with Fractions: Example 10	Equations with Fractions: Example 10 Topic Equations Description This example illustrates solving Equations with Fractions: Example 10 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 11	Equations with Fractions: Example 11 Topic Equations Description This example illustrates solving Equations with Fractions: Example 11 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 12	Equations with Fractions: Example 12 Topic Equations Description This example illustrates solving Equations with Fractions: Example 12 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 13	Equations with Fractions: Example 13 Topic Equations Description This example illustrates solving Equations with Fractions: Example 13 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 2	h1>Equations with Fractions: Example 2 Topic Equations	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 3	Equations with Fractions: Example 3 Topic Equations	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 4	Equations with Fractions: Example 4 Topic Equations Description This example illustrates solving Equations with Fractions: Example 4 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 5	Equations with Fractions: Example 5 Topic Equations Description This example illustrates solving Equations with Fractions: Example 5 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 6	Equations with Fractions: Example 6 Topic Equations Description This example illustrates solving Equations with Fractions: Example 6 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 7	Equations with Fractions: Example 7 Topic Equations Description This example illustrates solving Equations with Fractions: Example 7 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 8	Equations with Fractions: Example 8 Topic Equations Description This example illustrates solving Equations with Fractions: Example 8 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Equations with Fractions: Example 9	Equations with Fractions: Example 9 Topic Equations Description This example illustrates solving Equations with Fractions: Example 9 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra.	Solving Fraction Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 1	Extraneous Or No Solutions--Example 1 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 2	Extraneous Or No Solutions--Example 2 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 3	Extraneous Or No Solutions--Example 3 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 4	Extraneous Or No Solutions--Example 4 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 5	Extraneous Or No Solutions--Example 5 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 6	Extraneous Or No Solutions--Example 6 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--One-Variable Equations: Example 1	One-Variable Equations: Example 1 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 10	One-Variable Equations: Example 10 Topic Equations Description This example involves solving a one-variable equation that may include complex terms or require multiple steps to simplify. The equation might involve fractions, decimals, or variables on both sides. Solving it involves using inverse operations, distributing terms, and combining like terms to isolate the variable. This type of problem helps students refine their algebraic skills and understand the importance of systematic problem-solving. Checking the solution by substituting it back into the original equation is a crucial step to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 11	One-Variable Equations: Example 11 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 12	One-Variable Equations: Example 12 Topic Equations Description This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 13	One-Variable Equations: Example 13 Topic Equations Description This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 14	One-Variable Equations: Example 14 Topic Equations Description This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 15	One-Variable Equations: Example 15 Topic Equations Description This example involves solving a one-variable equation that may include complex terms or require multiple steps to simplify. The equation might involve fractions, decimals, or variables on both sides. Solving it involves using inverse operations, distributing terms, and combining like terms to isolate the variable. This type of problem helps students refine their algebraic skills and understand the importance of systematic problem-solving. Checking the solution by substituting it back into the original equation is a crucial step to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 16	One-Variable Equations: Example 16 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 17	One-Variable Equations: Example 17 Topic Equations Description This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 18	One-Variable Equations: Example 18 Topic Equations Description This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 19	One-Variable Equations: Example 19 Topic Equations Description This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 2	One-Variable Equations: Example 2 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 20	One-Variable Equations: Example 20 Topic Equations Description This example involves solving a one-variable equation that may include complex terms or require multiple steps to simplify. The equation might involve fractions, decimals, or variables on both sides. Solving it involves using inverse operations, distributing terms, and combining like terms to isolate the variable. This type of problem helps students refine their algebraic skills and understand the importance of systematic problem-solving. Checking the solution by substituting it back into the original equation is a crucial step to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 21	One-Variable Equations: Example 21 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 22	One-Variable Equations: Example 22 Topic Equations Description This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 23	One-Variable Equations: Example 23 Topic Equations Description This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 24	One-Variable Equations: Example 24 Topic Equations Description This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 25	One-Variable Equations: Example 25 Topic Equations Description This example involves solving a one-variable equation that may include complex terms or require multiple steps to simplify. The equation might involve fractions, decimals, or variables on both sides. Solving it involves using inverse operations, distributing terms, and combining like terms to isolate the variable. This type of problem helps students refine their algebraic skills and understand the importance of systematic problem-solving. Checking the solution by substituting it back into the original equation is a crucial step to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 26	One-Variable Equations: Example 26 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 27	One-Variable Equations: Example 27 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 3	One-Variable Equations: Example 3 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 4	One-Variable Equations: Example 4 Topic Equations Description This example likely demonstrates solving a more complex one-variable equation. It may involve multiple steps, such as combining like terms, using the distributive property, or dealing with fractions or decimals. The solving process typically includes isolating the variable on one side of the equation by performing inverse operations on both sides. This type of problem enhances students' algebraic manipulation skills and prepares them for more advanced equation solving. The specific solution would involve carefully following the order of operations and checking the final answer by substituting it back into the original equation.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 5	One-Variable Equations: Example 5 Topic Equations Description This example likely showcases a more challenging one-variable equation. It may involve variables on both sides of the equation, requiring students to consolidate like terms before solving. The problem might also include parentheses, necessitating the use of the distributive property. Solving this equation would involve carefully balancing operations on both sides, possibly dealing with negative numbers or fractions. This type of problem helps students develop their algebraic reasoning skills and reinforces the importance of maintaining equation balance throughout the solving process.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 6	One-Variable Equations: Example 6 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 7	One-Variable Equations: Example 7 Topic Equations Description This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 8	One-Variable Equations: Example 8 Topic Equations Description This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 9	One-Variable Equations: Example 9 Topic Equations Description This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 1	Solving Equations Using Angle Properties: Example 1 Topic Equations Description This example demonstrates solving equations using angle properties, specifically focusing on supplementary angles. Supplementary angles are two angles that add up to 180 degrees. In this case, we have one known angle of 135° and an unknown angle x. To solve such equations, we use the fundamental property of supplementary angles: their sum equals 180°.	Applications of Equations and Inequalities and Definition of an Angle
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 10	Solving Equations Using Angle Properties: Example 10 Topic Equations Description This example illustrates solving equations using angle properties, focusing on parallel lines cut by a transversal and supplementary angles. When parallel lines are cut by a transversal, pairs of supplementary angles are formed, meaning they sum to 180°. In this scenario, we have one known angle of 118° and an unknown angle x. However, angle y and the 118° angle are alternate exterior angles, which are congruent. This means we can set up this equation using the property of supplementary angles: 118 + x = 180	Applications of Equations and Inequalities and Definition of an Angle
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 2	Solving Equations Using Angle Properties: Example 2 Topic Equations Description This example illustrates solving equations using angle properties, focusing on supplementary angles. Supplementary angles are two angles that sum to 180 degrees. In this scenario, we have one known angle of 75° and an unknown angle x. The equation for supplementary angles is always in the form: angle1 + angle2 = 180°. Here, we can write 75 + x = 180. To solve for x, we subtract 75 from both sides: x = 180 - 75, giving us x = 105°.	Applications of Equations and Inequalities and Definition of an Angle
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 3	Solving Equations Using Angle Properties: Example 3 Topic Equations Description This example demonstrates solving equations using angle properties, specifically focusing on straight angles and vertical angles. A straight angle measures 180°, and vertical angles are always congruent. In this scenario, we have two known angles (36° and 72°) and an unknown angle x. This unknown angle x is vertical (and therefore congruent) to angle z. The angles 36, 72, and z form a straight, but since z is congruent to x, we can write the sum of this straight angle: x + 36 + 72 = 180 x = 72°	Applications of Equations and Inequalities and Definition of an Angle
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 4	Solving Equations Using Angle Properties: Example 4 Topic Equations Description This example illustrates solving equations using angle properties, focusing on straight angles and vertical angles. A straight angle measures 180°, and vertical angles are always congruent. In this scenario, we have two known angles (42° and 55°) and an unknown angle x. However, angle x is vertical (and therefore congruent) to angle y. The equation can be set up based on the fact that the sum of angles on a straight line is 180°. Thus, we have: 42 + 55 + x = 180	Applications of Equations and Inequalities and Definition of an Angle