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Big Ideas Math Integrated I, 2016 View details

4. Solving Absolute Value Equations

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Exercise 2 Page 28

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

Solutions: x=5 and x=- 3
Number Line:

Practice makes perfect

An absolute value measures an expression's distance from a midpoint on a number line. |x-1|= 4 This equation means that the distance is 4, either in the positive direction or the negative direction. |x-1|= 4 ⇒ lx-1= 4 x-1= - 4 To find the solutions to the absolute value equation, we need to solve both of these cases for x.

| x-1|=4

lc x-1 ≥ 0:x-1 = 4 & (I) x-1 < 0:x-1 = - 4 & (II)

lcx-1=4 & (I) x-1=- 4 & (II)

(I), (II): LHS+1=RHS+1

lx_1=5 x_2=- 3

Both 5 and - 3 are solutions to the absolute value equation. Let's graph these solutions on a number line.