Q47. - Algebra 2

Question

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

$\mathbf{-}\mathbf{1}<\mathbf{3}\left(\mathbf{y}\mathbf{-}\mathbf{2}\right)\le \mathbf{9}$

Step-by-Step Solution

Answer

Solution set of inequality is $\left\{\mathbf{y}\mathbf{|}\frac{\mathbf{5}}{\mathbf{3}}<\mathbf{y}\le \mathbf{5}\right\}$.

Solution set on number line is 

Step 1 - Write properties of inequality.

Properties of inequalities are written in following table:

Step 2 - Solve &#8722; 1 &#60; 3 y &#8722; 2 &#8804; 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.

 $\begin{array}{c}-1+6<3y-6+6\le 9+6\\ \frac{5}{3}<\frac{3y}{3}\le \frac{15}{3}\\ \frac{5}{3}<y\le 5\end{array}$

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

Step 3 &ndash; Graph the solution set.

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

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

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.