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Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
4. Solving Absolute Value Equations
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Exercise 16 Page 32

How many cases do we have after we remove the absolute value?

Solutions: q=22 and q=- 6
Number Line:

Practice makes perfect

An absolute value measures an expression's distance from a midpoint on a number line. |q-8|= 14 This equation means that the distance is 14, either in the positive direction or the negative direction. |q-8|= 14 ⇒ lq-8= 14 q-8= - 14 To find the solutions to the absolute value equation, we need to solve both of these cases for q.

|q-8|=14

lc q-8 ≥ 0:q-8 = 14 & (I) q-8 < 0:q-8 = - 14 & (II)

lcq-8=14 & (I) q-8=- 14 & (II)

(I), (II): LHS+8=RHS+8

lq_1=22 q_2=- 6

Both 22 and - 6 are solutions to the absolute value equation. Let's graph these solutions on a number line.

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arrow_right Communicate Your Answer p.27
4
Communicate Your Answer 5 (Page 27)
arrow_right Monitoring Progress p.28-31
Monitoring Progress 1 (Page 28)
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arrow_right Exercises p.32-34
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