Q45. - 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.

45. $\mathbf{8}\left(\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{1}\right)>\mathbf{11}\mathbf{x}\mathbf{-}\mathbf{17}$

Step-by-Step Solution

Answer

Solution set of inequality is $\mathbf{(}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{8}\mathbf{,}+\infty \mathbf{)}$.

Solution set on number line is 

Step 1 - Write properties of inequality.

Properties of inequalities are written in following table:

Step 2 - Solve 8 2 x − 1 > 11 x − 17 .

To solve given inequality, use subtraction, addition and division properties of inequality. Expand the left-hand side. Add 8 on each side then subtract $11x$ from each side and divide each side by 5 and simplify.

$\begin{array}{c}16x-8>11x-17\\ 16x-8+8>11x-17+8\\ 16x-11x>11x-9-11x\\ \frac{5x}{5}>\frac{-9}{5}\\ x>-1.8\end{array}$

Thus, solution is $x>-1.8$.

Step 3 – Describe solution set in interval notation.

As solution set of the inequality is all real numbers greater than $-1.8$.

Write the solution set in interval notation.

$(-1.8,+\infty )$

Step 4 – Graph the solution set.

Open circle on $-1.8$ shows this point is excluded in the solution set.