Question

Solve each inequality. Graph the solution set on a number line.

$\left|\mathbf{2}\mathbf{y}\mathbf{-}\mathbf{9}\right|\le \mathbf{27}$

Short answer

Solution set of inequality is $\left\{\mathbf{y}\mathbf{|}\mathbf{-}\mathbf{9}\le \mathbf{y}\le \mathbf{18}\right\}$.

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.

$\left|2y-9\right|\le 27$ is equivalent to $2y-9\le 27$ or $2y-9\ge -27$.

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

$\begin{array}{c}2y-9+9\le 27+9\\ \frac{2y}{2}\le \frac{36}{2}\\ y\le 18\end{array}$

– Description of step.

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

$\begin{array}{c}2y-9+9\ge -27+9\\ \frac{2y}{2}\ge \frac{-18}{2}\\ y\ge -9\end{array}$

Thus, solution is $y\le 18$or $y\ge -9$.

– 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, $\left\{y|-9\le y\le 18\right\}$.

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