Exercise 11 Page 211

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

Solutions: n=-4 or n=4
Graph:

Practice makes perfect

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

|n|+3=7

SubEqn

LHS-3=RHS-3

|n|+3-3=7-3

SubTerms

Subtract terms

|n|=4

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

This equation means that the distance is 4, either in the positive direction or the negative direction. |n|= 4 ⇒ ln= 4 n= -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.

|n|+3=7

Substitute

n= 4

| 4|+3? =7

AbsPos

|4|=4

4+3? =7

AddTerms

Add terms

7=7 ✓

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

|n|+3=7

Substitute

n= -4

| -4|+3? =7

AbsNeg

|-4|=4

4+3? =7

AddTerms

Add terms

7=7 ✓

Since the substitution resulted in an identity, n=-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 11 Page 211

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