Question

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line.

10. $\frac{n}{12}+15\le 13$

Short answer

Solution of inequality $\frac{n}{12}+15\le 13$is$n\le -24$

In set-builder form, solution set is$\left\{n|n\le -24\right\}$

Solution set on number line is

Step-by-step solution

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify n12+15≤13

To simplify given inequality, use subtraction and multiplication property of inequalities. Subtract by same number does not change the sign of inequality. Also multiply by same positive number does not change the sign of inequality as shown below

$\begin{array}{c}\frac{n}{12}+15\le 13\\ \frac{n}{12}+15-15\le 13-15\\ \frac{n}{12}\le -2\\ \frac{n}{12}\times 12\le -2\times 12\\ n\le -24\end{array}$

- Write solution set

The solution set of the inequality $n\le -24$ contains all real numbers less than or equal to $-24$

In set-builder form

Solution set is $\left\{n|n\le -24\right\}$

- Graph the solution set

Assolution set of the inequality$n\le -24$contains all real numbers less than or equal to$-24$

So arrow is towards $-\infty$and dot on $-24$denotes it is included in the solution set.