Exercise 13 Page 211

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

Solutions: x=-8 or x=8
Graph:

Practice makes perfect

Before we can solve this equation, we need to isolate the absolute value expression using the Properties of Equality.

|x|-10=-2

AddEqn

LHS+10=RHS+10

|x|-10+10=-2+10

AddTerms

Add terms

|x|=8

An absolute value measures an expression's distance from a midpoint on a number line. |x|= 8

This equation means that the distance is 8, either in the positive direction or the negative direction. |x|= 8 ⇒ lx= 8 x= -8 Both -8 and 8 are solutions to the absolute value equation. Let's graph these solutions on a number line.

To check our solutions, we will substitute them into the equation.

|x|-10=-2

Substitute

x= 8

| 8|-10? =-2

AbsPos

|8|=8

8-10? =-2

SubTerm

Subtract term

-2=-2 ✓

Since the substitution resulted in an identity, x=8 is a correct solution.

|x|-10=-2

Substitute

x= -8

| -8|-10? =-2

AbsNeg

|-8|=8

8-10? =-2

SubTerm

Subtract term

-2=-2 ✓

Because the substitution resulted in an identity, x=-8 is also a correct solution.

Subchapter links

Lesson Check p.210

Practice and Problem-Solving Exercises p.211-213

Standardized Test Prep p.213

Mixed Review p.213

Exercise 13 Page 211

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