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6.5 and 6.6 Solving Absolute Value Equations & Inequalities

6.5 and 6.6 Solving Absolute Value Equations & Inequalities. Page 322. 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. Ex: x = 5. What are the possible values of x?

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6.5 and 6.6 Solving Absolute Value Equations & Inequalities

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  1. 6.5 and 6.6 Solving Absolute Value Equations & Inequalities Page 322

  2. 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

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

  4. To solve an absolute value equation: ax+b = c, where c>0 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.

  5. 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!

  6. 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.

  7. Solving Absolute Value Inequalities • ax+b < c, where c>0 Becomes an “and” problem Changes to: –c<ax+b<c • ax+b > c, where c>0 Becomes an “or” problem Changes to: ax+b>c or ax+b<-c

  8. Ex: Solve & graph. • Becomes an “and” problem -3 7 8

  9. Solve & graph. • Get absolute value by itself first. • Becomes an “or” problem -2 3 4

  10. Assignment

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