Chapter 2: Q. 400 (page 195)

Solve each inequality, graph the solution, and write the solution in interval notation.
$- 8 < 5 x + 2 \leq - 3$

Short Answer

Expert verified

Solution of inequality:

$- 2 < x \leq - 1$

Graph the numbers that make both inequalities true:

The solution in interval notation:

$(- 2, - 1]$

Step by step solution

Step 1. Given information

Consider the inequality

$- 8 < 5 x + 2 \leq - 3$

Step 2. Solve the inequality −8 < 5x + 2 ≤ −3

Subtract 2 to all three parts:

$- 8 - 2 < 5 x + 2 - 2 \leq - 3 - 2$

Simplify:

$- 10 < 5 x \leq - 5$

Divide each part by 5:

$\frac{- 10}{5} < \frac{5 x}{5} \leq \frac{- 5}{5}$

Simplify:

$- 2 < x \leq - 1$

Step 3. Graph the solution of inequality −2 < x ≤ −1

The solution in interval notation:

$(- 2, - 1]$

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Solve each inequality, graph the solution, and write the solution in interval notation.
$- 8 < 5 x + 2 \leq - 3$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the inequality −8 < 5x + 2 ≤ −3

Step 3. Graph the solution of inequality −2 < x ≤ −1

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Solve each inequality, graph the solution, and write the solution in interval notation. −8<5x+2≤−3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the inequality −8 < 5x + 2 ≤ −3

Step 3. Graph the solution of inequality −2 < x ≤ −1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Decision Maths

Pure Maths

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

Solve each inequality, graph the solution, and write the solution in interval notation.
$- 8 < 5 x + 2 \leq - 3$