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Chapter 5: Q36. (page 324)

Solve each inequality. Then graph the solution set.

|p+2|>7

Short Answer

Expert verified

The solution for the given inequality p+2>7is p∈−∞,−9∪5,∞.

The graph of the solution set which isp∈−∞,−9∪5,∞ is:

Step by step solution

01

Step 1. Solve the given inequality |p+2|>7.

The solution of the given inequalityp+2>7 is:

Case 1:p+2 is non-negative.

p+2>7p+2−2>7−2p>5p∈5,∞

Case 2:p+2 is negative.

−p+2>7−1−p+2<−17p+2<−7p+2−2<−7−2p<−9p∈−∞,−9

The solution of the inequalityx≥a isx≤−a or x≥a.

That implies the solution of the inequalityx≥ais the union of the solutions of the inequalities x≤−aand x≥a.

Find the union of the solutions of the inequalitiesp+2>7 andp+2<−7 to find the solution of the inequality p+2>7.

The union of the solutions of the inequalitiesp+2>7 andp+2<−7 is:

p∈−∞,−9∪5,∞

Therefore, the solution of the inequalityp+2>7 is p∈−∞,−9∪5,∞.

02

Step 2. Draw the graph of the solution set which is p∈(−∞,−9)∪(5,∞).

The graph of the solution set which is p∈−∞,−9∪5,∞is:

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Most popular questions from this chapter

Solve each inequality. Then graph it on a number line.

13−p≥15

Solvex−4<2

Define a variable, write an inequality, and solve each problem. Check your solution.

Twice a number increased by 3 is less than the number decreased by 4.

Record your answers on a sheet of paper. Show your work.

Theresa is saving money for a vacation. She needs to save at least \(640 to pay for her expenses. Each week, she puts 19 \)35towards her vacation savings.

a. Let role="math" localid="1647838507456" wrepresent the number of weeks Theresa saves money. Write an inequality to model the situation.

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Solve each inequality. Check your solution.

3c−7<11
See all solutions

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