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Mastering Absolute Value Equations: Step-by-Step Guide

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This resource provides students with clear instructions on solving equations involving absolute values. It covers essential examples such as 7x = 56 and 3y + 7 = 19, emphasizing the process of isolating the absolute value before splitting into two equations. The guide illustrates how to handle different scenarios and includes practice problems to reinforce learning. Students will also find key strategies to check their solutions effectively. Perfect for enhancing understanding in algebra and preparing for homework assignments.

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Mastering Absolute Value Equations: Step-by-Step Guide

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  1. Warm Up Solve each equation for the given variable. 7x = 56 2) 3y + 7 = 19 3) 4 – 2x = 16 4) x – 9 = -22

  2. 6-5 Solving Absolute Value Equations Standard 3.0: Students solve equations and inequalities involving absolute value.

  3. Absolute Value (of x) • Symbol lxl • The distance x is from 0 on the number line. • Always positive • Ex: l-3l=3 -4 -3 -2 -1 0 1 2

  4. Ex: x = 5 • What are the possible values of x? x = 5 or x = -5

  5. Try It Out!

  6. To solve an absolute value equation: ax+b = c, where c>0 *C cannot be negative To solve, set up 2 new equations, then solve each equation. ax+b = c or ax+b = -c ** make sure the absolute value is by itself before you split to solve.

  7. Ex: Solve 6x-3 = 15 6x-3 = 15 or 6x-3 = -15 6x = 18 or 6x = -12 x = 3 or x = -2 * Plug in answers to check your solutions!

  8. Ex: Solve 2x + 7 -3 = 8 Get the abs. value part by itself first! 2x+7 = 11 Now split into 2 parts. 2x+7 = 11 or 2x+7 = -11 2x = 4 or 2x = -18 x = 2 or x = -9 Check the solutions.

  9. Try It Out! • Solve each equation.

  10. Homework Assignment • Page 325 #7 – 18 All

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