Chapter 1: Q47. (page 50)

Solve each inequality. Graph the solution set on a number line.
$- 1 < 3 (y - 2) \leq 9$

Short Answer

Expert verified

Solution set of inequality is $\{y | \frac{5}{3} < y \leq 5\}$ .

Solution set on number line is

Step by step solution

- Write properties of inequality.

Properties of inequalities are written in following table:

- Solve −1<3y−2≤9.

To solve given inequality, use Addition and division properties of inequality. Expand the middle part. Add 6 on each part then divide each part by 3 and simplify.

$\begin{matrix} - 1 + 6 < 3 y - 6 + 6 \leq 9 + 6 \\ \frac{5}{3} < \frac{3 y}{3} \leq \frac{15}{3} \\ \frac{5}{3} < y \leq 5 \end{matrix}$

Thus, solution is $\frac{5}{3} < y \leq 5$ .

– Graph the solution set.

Assolution set of the inequality is all real numbers greater than $\frac{5}{3}$ or less than or equal to 5.

The solution set is, $\{y | \frac{5}{3} < y \leq 5\}$ .

Open circle on $\frac{5}{3}$ shows this point is excluded in the solution set and closed circle on 5 shows this point is included in the solution set.

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Solve each inequality. Graph the solution set on a number line.
$- 1 < 3 (y - 2) \leq 9$

Short Answer

Step by step solution

- Write properties of inequality.

- Solve −1<3y−2≤9.

– Graph the solution set.

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Solve each inequality. Graph the solution set on a number line.-1<3y-2≤9

Short Answer

Step by step solution

- Write properties of inequality.

- Solve −1<3y−2≤9.

– Graph the solution set.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set on a number line.
$- 1 < 3 (y - 2) \leq 9$