Chapter 5: Q31. (page 324)

Solve each compound inequality. Then graph the solution set.
$m - 3 < 6$ and $m + 2 > 4$

Short Answer

Expert verified

The solution of the given compound inequality $m - 3 < 6$ and $m + 2 > 4$ is $m \in (2, 9)$ .

The graph of the solution set which is $m \in (2, 9)$ is:

Step by step solution

Step 1. Solve the given compound inequality m−3<6 and m+2>4.

The solution of the given compound inequality $m - 3 < 6$ and $m + 2 > 4$ is:

Solve the inequality $m - 3 < 6$ .

$m - 3 < 6 m - 3 + 3 < 6 + 3 m < 9 m \in (- \infty, 9)$

Solve the inequality $m + 2 > 4$ .

$m + 2 > 4 m + 2 - 2 > 4 - 2 m > 2 m \in (2, \infty)$

A compound inequality containing ‘and’ is true if both inequalities are true.

That implies the solution of the compound inequality containing ‘and’ is the intersection of the solutions of the two simple statements.

Find the intersection of the solutions of the inequalities $m - 3 < 6$ and $m + 2 > 4$ to find the solution of the compound inequality $m - 3 < 6$ and $m + 2 > 4$ .

The intersection of the solutions of the inequalities $m - 3 < 6$ and $m + 2 > 4$ is:

$m \in (2, 9)$

Therefore, the solution of the compound inequality $m - 3 < 6$ and $m + 2 > 4$ is $m \in (2, 9)$ .

Step 2. Draw the graph of the solution set which is m∈2,9.

The graph of the solution set which is $m \in (2, 9)$ is:

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Solve each compound inequality. Then graph the solution set.
$m - 3 < 6$ and $m + 2 > 4$

Short Answer

Step by step solution

Step 1. Solve the given compound inequality m−3<6 and m+2>4.

Step 2. Draw the graph of the solution set which is m∈2,9.

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Solve each compound inequality. Then graph the solution set.m−3<6andm+2>4

Short Answer

Step by step solution

Step 1. Solve the given compound inequality m−3<6 and m+2>4.

Step 2. Draw the graph of the solution set which is m∈2,9.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Solve each compound inequality. Then graph the solution set.
$m - 3 < 6$ and $m + 2 > 4$