Exercise 33 Page 33

Example Solution: |x-5.5|=3.5

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 2 and 9 is 5.5, and that the distance from both values to the midpoint is 3.5. Let's write our equation. |x-Midpoint|&= Distance to midpoint |x- 5.5|&= 3.5 We can solve the equation we have created to ensure it has the desired solutions.

|x-5.5|=3.5

lc x-5.5 ≥ 0:x-5.5 = 3.5 & (I) x-5.5 < 0:x-5.5 = - 3.5 & (II)

lcx-5.5=3.5 & (I) x-5.5=- 3.5 & (II)

(I), (II): LHS+5.5=RHS+5.5

lx_1=9 x_2=2

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 33 Page 33

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