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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

7. Absolute Value Equations and Inequalities

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Exercise 40 Page 211

Create an or compound inequality because the absolute value is greater than the given value.

Solution Set: w<-3 or w> 52
Graph:

Practice makes perfect

We are asked to find and graph the solution set for all possible values of w in the given inequality. |4w+1|>11 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number that makes the distance between 4w and -1 greater than 11 in the positive direction or in the negative direction. 4w+1 >11 or 4w+1< -11

Let's isolate w in both of these cases before graphing the solution set.

Case 1

4w+1>11

LHS-1>RHS-1

4w>10

.LHS /4.>.RHS /4.

w>10/4

a/b=.a /2./.b /2.

w>5/2

This inequality tells us that all values greater than 52 will satisfy the inequality.

Case 2

4w+1<-11

LHS-1

4w<-12

.LHS /4.<.RHS /4.

w<-3

This inequality tells us that all values less than -3 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& w>5/2 [0.8em] Second Solution Set:& w<-3 Combined Solution Set:& w<-3 or w>5/2 [0.8em]

Graph

The graph of this inequality includes all values less than -3 or greater than 52. We show this by keeping the endpoints open.

Subchapter links

Lesson Check p.210

Practice and Problem-Solving Exercises p.211-213

Standardized Test Prep p.213

Mixed Review p.213