Q62. - 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.

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

 

Step-by-Step Solution

Answer

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

Solution set on number line is 

Step 1 - Write properties of inequality.

Properties of inequalities are written in following table:

Step 2 - Solve 7 x + 11 > 9 x + 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$4>x$.

Step 3 – Describe solution set in interval notation.

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

Write the solution set in interval notation.

 

$(-\infty ,4)$

Step 4 – Graph the solution set.

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