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Big Ideas Math Integrated I, 2016 View details

4. Solving Absolute Value Equations

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Exercise 18 Page 32

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

Solutions: t=12 and t=- 12
Number Line:

Practice makes perfect

An absolute value measures an expression's distance from a midpoint on a number line. |t/2|= 6 This equation means that the distance is 6, either in the positive direction or the negative direction. t/2= 6 and t/2= - 6 To find the solutions to the absolute value equation, we need to solve both of these cases for t.

|t/2|=6

lc t2 ≥ 0: t2 = 6 & (I) t2 < 0: t2 = - 6 & (II)

lc t2=6 & (I) t2=-6 & (II)

(I), (II): LHS * 2=RHS* 2

lt_1=12 t_2=-12

Both 12 and - 12 are solutions to the absolute value equation. Let's graph these solutions on a number line.