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--Quadratics--Solving Simple Quadratic Equations--Example 1	Solving Simple Quadratic Equations--Example 1 Topic Quadratics Description This example demonstrates solving a simplified form of a quadratic equation. The equation is in the form ax² = c, where the linear term (bx) is absent. This simplification allows for a straightforward solution by isolating x² and then taking the square root of both sides. The process is more direct than using the quadratic formula, making it easier to solve mentally or with minimal calculations. This method highlights the importance of recognizing special forms of quadratic equations for efficient problem-solving.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Simple Quadratic Equations--Example 2	Solving Simple Quadratic Equations--Example 2 Topic Quadratics Description This example showcases another simplified quadratic equation. The equation is in a form where factoring or using the square root method is straightforward. By recognizing this simpler structure, students can solve the equation without resorting to more complex techniques. This approach emphasizes the importance of identifying the most efficient method based on the equation's form, promoting problem-solving skills and mathematical intuition.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Simple Quadratic Equations--Example 3	Solving Simple Quadratic Equations--Example 3 Topic Quadratics Description In this example, the quadratic equation is presented in a simplified form that allows for direct solving. The structure of the equation makes it possible to solve without using the quadratic formula or complex factoring techniques. This straightforward approach highlights how recognizing certain forms of quadratic equations can lead to quicker and more intuitive solutions, enhancing problem-solving efficiency.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Simple Quadratic Equations--Example 4	Solving Simple Quadratic Equations--Example 4 Topic Quadratics Description This example illustrates solving a quadratic equation in a simplified form. The equation's structure allows for a direct solution method, avoiding the need for more complex techniques like the quadratic formula. By recognizing this simpler form, students can apply basic algebraic skills to solve the equation efficiently, reinforcing the importance of identifying the most appropriate solving method based on the equation's characteristics.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Simple Quadratic Equations--Example 5	Solving Simple Quadratic Equations--Example 5 Topic Quadratics Description This example demonstrates solving a quadratic equation in a simplified form that allows for straightforward solution methods. The equation's structure enables direct solving techniques, bypassing the need for more complex approaches. This simplified form emphasizes the importance of recognizing patterns in quadratic equations, allowing for more efficient problem-solving and deepening understanding of quadratic relationships.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Simple Quadratic Equations--Example 6	Solving Simple Quadratic Equations--Example 6 Topic Quadratics Description In this example, a simplified form of a quadratic equation is presented, allowing for a more direct solving approach. The equation's structure makes it possible to apply basic algebraic techniques without resorting to complex methods. This straightforward solution process highlights the importance of recognizing special forms of quadratic equations, enabling students to choose the most efficient solving strategy.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Simple Quadratic Equations--Example 7	Solving Simple Quadratic Equations--Example 7 Topic Quadratics Description This example showcases solving a quadratic equation in a simplified form that allows for direct solution methods. The equation's structure enables the use of basic algebraic techniques, avoiding the need for more complex approaches like the quadratic formula. This simplified approach emphasizes the importance of identifying the most efficient solving method based on the equation's form, enhancing problem-solving skills and mathematical intuition.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Simple Quadratic Equations--Example 8	Solving Simple Quadratic Equations--Example 8 Topic Quadratics Description In this final example, a simplified quadratic equation is presented, demonstrating how certain forms allow for straightforward solving techniques. The equation's structure enables direct solution methods, bypassing the need for complex approaches. This example reinforces the importance of recognizing special forms of quadratic equations, allowing students to apply the most efficient solving strategy and deepen their understanding of quadratic relationships.	Quadratic Equations and Functions
Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 1	Equations Using the Exterior Angle Theorem--Example 1 Topic Equations	Applications of Triangles
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