Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative Numbers

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 10	Equations Using the Exterior Angle Theorem--Example 10 Topic Equations Description This example illustrates a more complex application of the Exterior Angle Theorem in solving triangle-related equations. In this scenario, we have a triangle with one known interior angle of 35°, an unknown interior angle y, and an unknown exterior angle x. The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Here, the equation is set up as x = 35° + y. Furthermore, the angles 3x and x are supplementary, allowing you to solve for x. Having solved for x, you can then solve for y.	Applications of Triangles
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 2	Equations Using the Exterior Angle Theorem--Example 2 Topic Equations	Applications of Triangles
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 3	Equations Using the Exterior Angle Theorem--Example 3 Topic Equations	Applications of Triangles
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 4	Equations Using the Exterior Angle Theorem--Example 4 Topic Equations	Applications of Triangles
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 5	Equations Using the Exterior Angle Theorem--Example 5 Topic Equations	Applications of Triangles
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 6	Equations Using the Exterior Angle Theorem--Example 6 Topic Equations	Applications of Triangles
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 7	Equations Using the Exterior Angle Theorem--Example 7 Topic Equations	Applications of Triangles
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 8	Equations Using the Exterior Angle Theorem--Example 8 Topic Equations	Applications of Triangles
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 9	Equations Using the Exterior Angle Theorem--Example 9 Topic Equations Description This example presents a more challenging application of the Exterior Angle Theorem in solving triangle-related equations. In this scenario, we have a triangle with one known interior angle of 25°, an unknown interior angle y, and an unknown exterior angle x. The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Here, the equation is set up as x = 25° + y. You can also use the fact that x and 2x are supplementary, allowing you to solve for x. By solving for x, you can then solve for y using the triangle equation.	Applications of Triangles
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 1	Equations with Angles from Parallel Lines Cut by a Transversal--Example 1 Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 10	Equations with Angles from Parallel Lines Cut by a Transversal--Example 10 Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 2	Equations with Angles from Parallel Lines Cut by a Transversal--Example 2 Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 3	Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 4	Equations with Angles from Parallel Lines Cut by a Transversal--Example 4 Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 5	Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 6	Equations with Angles from Parallel Lines Cut by a Transversal--Example 6 Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 7	Equations with Angles from Parallel Lines Cut by a Transversal--Example 7 Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 8	Equations with Angles from Parallel Lines Cut by a Transversal--Example 8 Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 9	Equations with Angles from Parallel Lines Cut by a Transversal--Example 9 Topic Equations	Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities
Math Example--Solving Equations--Equations with Fractions: Example 1	Equations with Fractions: Example 1 Topic Equations	Solving Fraction Equations
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