body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Pearson Algebra 1 Common Core, 2011

PA

Pearson Algebra 1 Common Core, 2011 View details

7. Absolute Value Equations and Inequalities

Continue to next subchapter

Exercise 5 Page 210

Create an or compound inequality because the absolute value needs to be greater than or equal to the given value.

Solution Set: x≤-3 or x≥-1
Graph:

Practice makes perfect

We are asked to find and graph the solution set for all possible values of x in the given inequality. |x+2|≥1 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 x and -2 greater than or equal to 1 in the positive direction or in the negative direction. x+2 ≥ 1 or x+2≤ -1

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

Case 1

x+2 ≥ 1

LHS-2≥RHS-2

x≥ -1

This inequality tells us that all values greater than or equal to -1 will satisfy the inequality.

Case 2

x+2 ≤ -1

LHS-2≤RHS-2

x≤-3

This inequality tells us that all values less than or equal to -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:& x≥-1 Second Solution Set:& x≤ -3 Combined Solution Set:& x≤ -3 or x≥ -1

Graph

The graph of this inequality includes all values less than or equal to - 3 or greater than or equal to -1. We show this by keeping the endpoints closed.

Subchapter links

Lesson Check p.210

Practice and Problem-Solving Exercises p.211-213

Standardized Test Prep p.213

Mixed Review p.213