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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 41 Page 211

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

Solution Set: t≤-2.4 or t≥4
Graph:

Practice makes perfect

We are asked to find and graph the solution set for all possible values of t in the given inequality. |5t-4|≥ 16 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 5t and 4 greater than or equal to 16 in the positive direction or in the negative direction. 5t-4 ≥ 16 or 5t-4≤ -16

Let's isolate t in both of these cases before graphing the solution set.

Case 1

5t-4≥ 16

LHS+4≥RHS+4

5t≥20

.LHS /5.≥.RHS /5.

t≥4

This inequality tells us that all values greater than or equal to 4 will satisfy the inequality.

Case 2

5t-4≤ -16

LHS+4≤RHS+4

5t≤-12

.LHS /5.≤.RHS /5.

t≤ -2.4

This inequality tells us that all values less than or equal to -2.4 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& t≥4 Second Solution Set:& t≤ -2.4 Combined Solution Set:& t≤ -2.4 or t≥4

Graph

The graph of this inequality includes all values less than or equal to -2.4 or greater than or equal to 4. 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