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Solving Absolute Value Equations 6.5

Solving Absolute Value Equations 6.5. Absolute Value (of x). Symbol |x| The distance x is from 0 on the number line. Always positive Ex: |-3|= 3. -4 -3 -2 -1 0 1 2. Ex: x = 5. What are the possible values of x? x = 5 or x = -5.

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Solving Absolute Value Equations 6.5

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  1. Solving Absolute Value Equations6.5

  2. Absolute Value (of x) • Symbol |x| • The distance x is from 0 on the number line. • Always positive • Ex: |-3|= 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: • Isolate the absolute value expression • Remove the bars and write as two separate equations— one equal to positive, one equal to negative • Solve each equation • Check your answers 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. Ex: Solve 2 4m + 10 = 12m Get the abs. value part by itself first! 4m+10 = 6m Now split into 2 parts. 4m+10 = 6m or 4m+10 = -6m 10 = 2m or 10 = -10m m = 5 or m = -1 Check the solutions. -1 is an extraneous solution

  8. Homework: • p.393 #3-30 multiples of 3

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