Exercise 15 Page 211

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

Solutions: m=-3 or m=3
Graph:

Practice makes perfect

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

-3|m|=-9

DivEqn

.LHS /(-3).=.RHS /(-3).

-3|m|/-3=-9/-3

DivNegNeg

- a/- b=a/b

|m|=3

An absolute value measures an expression's distance from a midpoint on a number line. |m|= 3

This equation means that the distance is 3, either in the positive direction or the negative direction. |m|= 3 ⇒ lm= 3 m= -3 Both 3 and -3 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.

-3|m|=-9

Substitute

m= 3

-3| 3|? =-9

AbsPos

|3|=3

-3(3)? =-9

MultNegPos

(- a)b = - ab

-9=-9 ✓

Since the substitution resulted in an identity, m=3 is a correct solution.

-3|m|=-9

Substitute

m= -3

-3| -3|? =-9

AbsNeg

|-3|=3

-3(3)? =-9

MultNegPos

(- a)b = - ab

-9=-9 ✓

Because the substitution resulted in an identity, m=-3 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 15 Page 211

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