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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 35 Page 211

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

Solution Set: y≤-11 or y≥-5
Graph:

Practice makes perfect

We are asked to find and graph the solution set for all possible values of y in the given inequality. |y+8|≥ 3 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 y and -8 greater than or equal to 3 in the positive direction or in the negative direction. y+8 ≥ 3 or y+8≤ - 3

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

Case 1

y+8≥ 3

LHS-8≥RHS-8

y≥ -5

This inequality tells us that all values greater than or equal to -5 will satisfy the inequality.

Case 2

y+8 ≤ -3

LHS-8≤RHS-8

y≤ -11

This inequality tells us that all values less than or equal to -11 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& y≥-5 Second Solution Set:& y≤ -11 Combined Solution Set:& y≤ -11 or y≥ -5

Graph

The graph of this inequality includes all values less than or equal to - 11 or greater than or equal to -5. 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