Question

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

42. $\frac{\mathbf{n}}{\mathbf{12}}\mathbf{+}\mathbf{5}\le \mathbf{7}$

Short answer

Solution set of inequality is $\mathbf{(}\mathbf{-}\infty \mathbf{,}\mathbf{24}\mathbf{]}$.

Solution set on number line is

Step-by-step solution

- Write properties of inequality.

Properties of inequalities are written in following table:

- Solve n12+5≤7.

To solve given inequality, use subtraction and multiplication properties of inequality. Subtract 5 from both the sides then multiply each side by 12 and simplify.

$\begin{array}{c}\frac{n}{12}+5-5\le 7-5\\ \frac{n}{12}\cdot 12\le 2\cdot 12\\ n\le 24\end{array}$

Thus, solution is $n\le 24$.

– Describe solution set in interval notation.

Assolution set of the inequality is all real numbers less than or equal to 24.

Write the solution set in interval notation.

$(-\infty ,24]$

– Graph the solution set.

Closed circle on 24 shows this point is included in the solution set.