Exercise 32 Page 33

Example Solution: |x-2|=8

Practice makes perfect

To write an absolute value equation, we can begin by thinking about the solutions to the equation as points on a number line. We can use the number line to determine the midpoint and the distance from each point to the midpoint. Our equation will take the following form. |x-Midpoint|=Distance to midpoint Let's plot the given solutions on a number line and determine the midpoint.

From the number line, we can see that the midpoint between - 6 and 10 is 2, and that the distance from both values to the midpoint is 8. Let's write our equation. |x-Midpoint|&= Distance to midpoint |x- 2|&= 8 We can solve the equation we have created to ensure it has the desired solutions.

|x-2|=8

lc x-2 ≥ 0:x-2 = 8 & (I) x-2 < 0:x-2 = - 8 & (II)

lcx-2=8 & (I) x-2=- 8 & (II)

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

lx_1=10 x_2=- 6

Keep in mind that this is just one possible absolute value equation we could use.

Subchapter links

Communicate Your Answer p.27

Monitoring Progress p.28-31

Exercises p.32-34

Exercise 32 Page 33

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