Chapter 1: Q39. (page 44)

Solve each inequality. Graph the solution set on a number line.
$|3 w + 2| \leq 5$

Short Answer

Expert verified

Solution of inequality is $- \frac{7}{3} \leq w and w \leq 1$

Solution set in number line is

Step by step solution

- Definition of absolute value inequality

For real numbers $a and b$ with b>0

Absolute value inequality is $|a| < b$ when $- b < a and a < b$ , and

Absolute value inequality is $|a| > b$ when $a < - b or a > b$

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify 3w+2≤5

From definition of absolute value inequality, given expression is simplified to

" width="9" height="19" role="math">−5≤3w+2and3w+2≤5

Use subtraction and division property of inequality, subtract with same number does not change the sign of inequality. Also division by same positive number does not reverse the sign of inequality as shown below

$\begin{matrix} - 5 - 2 \leq 3 w + 2 - 2 and 3 w + 2 - 2 \leq 5 - 2 \\ - 7 \leq 3 w and 3 w \leq 3 \\ - \frac{7}{3} \leq \frac{3 w}{3} and \frac{3 w}{3} \leq \frac{3}{3} \\ - \frac{7}{3} \leq w and w \leq 1 \end{matrix}$

- Graph the solution set

For $- \frac{7}{3} \leq w and w \leq 1$ , number line starts from $- \frac{7}{3}$ to 1

Dot on $- \frac{7}{3} and 1$ shows these points are included in the solution.

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Year	Average CPI
1950	42.1
1960	29.6
1970	38.8
1980	82.4
1990	130.7
2000	174.0

Solve each inequality. Graph the solution set on a number line.
$|3 w + 2| \leq 5$

Short Answer

Step by step solution

- Definition of absolute value inequality

- Write properties of inequality

- Simplify 3w+2≤5

- Graph the solution set

One App. One Place for Learning.

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Solve each inequality. Graph the solution set on a number line.3w+2≤5

Short Answer

Step by step solution

- Definition of absolute value inequality

- Write properties of inequality

- Simplify 3w+2≤5

- Graph the solution set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Logic and Functions

Applied Mathematics

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set on a number line.
$|3 w + 2| \leq 5$