Q43. - Algebra 2

Question

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

$\mathbf{3}\left(\mathbf{6}\mathbf{-}\mathbf{5}\mathbf{a}\right)<\mathbf{12}\mathbf{a}\mathbf{-}\mathbf{36}$

Step-by-Step Solution

Answer

Solution set of inequality is $\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{+}\infty \mathbf{)}$.

Solution set on number line is 

Step 1 - Write properties of inequality.

Properties of inequalities are written in following table:

Step 2 - Solve 3 6 &#8722; 5 a &#60; 12 a &#8722; 36 .

To solve given inequality, use subtraction and division properties of inequality. Expand the left-hand side. Add 36 on each side then add $15a$ on each side and divide each side by 27 and simplify.

 $\begin{array}{c}18-15a+36<12a-36+36\\ 54-15a+15a<12a+15a\\ \frac{54}{27}<\frac{27a}{27}\\ 2<a\end{array}$

Thus, solution is $2<a$.

Step 3 &ndash; Describe solution set in interval notation.

As solution set of the inequality is all real numbers greater than 2.

Write the solution set in interval notation.

$(2,+\infty )$

Step 4 &ndash; Graph the solution set.

Open circle on 2 shows this point is excluded in the solution set.