Exercise 14 Page 211

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

Solutions: d=-4 or d=4
Graph:

Practice makes perfect

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

5|d|=20

DivEqn

.LHS /5.=.RHS /5.

5|d|/5=20/5

CalcQuot

Calculate quotient

|d|=4

An absolute value measures an expression's distance from a midpoint on a number line. |d|= 4

This equation means that the distance is 4, either in the positive direction or the negative direction. |d|= 4 ⇒ ld= 4 d= -4 Both 4 and -4 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.

5|d|=20

Substitute

d= 4

5| 4|? =20

AbsPos

|4|=4

5(4)? =20

Multiply

20=20 ✓

Since the substitution resulted in an identity, d=4 is a correct solution.

5|d|=20

Substitute

d= -4

5| -4|? =20

AbsNeg

|-4|=4

5(4)? =20

Multiply

20=20 ✓

Because the substitution resulted in an identity, d=-4 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 14 Page 211

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