Q46. - Algebra 2

Question

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

46. $\mathbf{-}\mathbf{1}<\mathbf{3}\mathbf{a}\mathbf{+}\mathbf{2}<\mathbf{14}$

Step-by-Step Solution

Answer

Solution set of inequality is $\left\{\mathbf{a}\mathbf{|}\mathbf{-}\mathbf{1}<\mathbf{a}<\mathbf{4}\right\}$.

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 a + 2 &#60; 14 .

To solve given inequality, use subtraction and division properties of inequality. Subtract 2 from each part then divide each part by 3 and simplify.

$\begin{array}{c}-1-2<3a+2-2<14-2\\ \frac{-3}{3}<\frac{3a}{3}<\frac{12}{3}\\ -1<a<4\end{array}$

Thus, solution is $-1<a<4$.

Step 3 &ndash; Graph the solution set.

As solution set of the inequality is all real numbers greater than $-1$ or less than 4.

The solution set is, $\left\{a|-1<a<4\right\}$.

Open circles on $-1$ and 4 shows these points are excluded in the solution set.