Exercise 12 Page 211

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

Solutions: s=-10 or s=10
Graph:

Practice makes perfect

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

7=|s|-3

AddEqn

LHS+3=RHS+3

7+3=|s|-3+3

AddTerms

Add terms

10=|s|

RearrangeEqn

Rearrange equation

|s|=10

An absolute value measures an expression's distance from a midpoint on a number line. |s|= 10

This equation means that the distance is 10, either in the positive direction or the negative direction. |s|= 10 ⇒ ls= 10 s= -10 Both 10 and -10 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.

7=|s|-3

Substitute

s= 10

7? =| 10|-3

AbsPos

|10|=10

7? =10-3

SubTerm

Subtract term

7=7 ✓

Since the substitution resulted in an identity, s=10 is a correct solution.

7=|s|-3

Substitute

s= -10

7? =| -10|-3

AbsNeg

|-10|=10

7? =10-3

SubTerm

Subtract term

7=7 ✓

Since the substitution resulted in an identity, s=-10 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 12 Page 211

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