Chapter 1: Q49. (page 50)

Solve each inequality. Graph the solution set on a number line.
$|2 y - 9| \leq 27$

Short Answer

Expert verified

Solution set of inequality is $\{y | - 9 \leq y \leq 18\}$ .

Solution set on number line is

Step by step solution

- Write properties of inequality.

Properties of inequalities are written in following table:

- Solve 2y-9≤27.

$|2 y - 9| \leq 27$ is equivalent to $2 y - 9 \leq 27$ or $2 y - 9 \geq - 27$ .

Consider, $2 y - 9 \leq 27$ . Add 9 on each part then divide each part by 2 and simplify.

$\begin{matrix} 2 y - 9 + 9 \leq 27 + 9 \\ \frac{2 y}{2} \leq \frac{36}{2} \\ y \leq 18 \end{matrix}$

– Description of step.

Consider, $2 y - 9 \geq - 27$ . Add 9 on each part then divide each part by 2 and simplify.

$\begin{matrix} 2 y - 9 + 9 \geq - 27 + 9 \\ \frac{2 y}{2} \geq \frac{- 18}{2} \\ y \geq - 9 \end{matrix}$

Thus, solution is $y \leq 18$ or $y \geq - 9$ .

– Graph the solution set.

Assolution set of the inequality is all real numbers greater than or equal to -9 or less than or equal to 18.

The solution set is, $\{y | - 9 \leq y \leq 18\}$ .

Closed circles on $- 9$ and 18 shows these points are included in the solution set.

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Solve each inequality. Graph the solution set on a number line.
$|2 y - 9| \leq 27$

Short Answer

Step by step solution

- Write properties of inequality.

- Solve 2y-9≤27.

– Description of step.

– Graph the solution set.

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Solve each inequality. Graph the solution set on a number line.2y-9≤27

Short Answer

Step by step solution

- Write properties of inequality.

- Solve 2y-9≤27.

– Description of step.

– Graph the solution set.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set on a number line.
$|2 y - 9| \leq 27$