Question

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

$\mathbf{7}\mathbf{x}\mathbf{+}\mathbf{11}>\mathbf{9}\mathbf{x}\mathbf{+}\mathbf{3}$

Short answer

Solution set of inequality is $\mathbf{(}\mathbf{-}\infty \mathbf{,}\mathbf{4}\mathbf{)}$.

Solution set on number line is

Step-by-step solution

- Write properties of inequality.

Properties of inequalities are written in following table:

- Solve 7x+11>9x+3.

To solve given inequality, use subtraction and division properties of inequality. Subtract $7x$then 3 from each side and do not change the sign of inequality. Then divide each side by 2 and simplify.

$\begin{array}{l}7x+11-7x>9x+3-7x\\ 11-3>2x+3-3\\ \frac{8}{2}>\frac{2x}{2}\\ 4>x\end{array}$

Thus, solution is$4>x$.

– Describe solution set in interval notation.

Assolution set of the inequality is all real numbers less than 4.

Write the solution set in interval notation.

$(-\infty ,4)$

– Graph the solution set.

Open circle on 4 shows this point is excluded in the solution set.