Question

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

$5x<35$

Short answer

Solution of inequality $5x<35$ is $x<7$

In interval form, solution set is $\left(-\infty ,7\right)$

Solution set on number line is

Step-by-step solution

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify 5x<35

To simplify given inequality, use division property of inequalities. Divide by same positive number does not change the sign of inequality as shown below

$\begin{array}{c}5x<35\\ \frac{5x}{5}<\frac{35}{5}\\ x<7\end{array}$

- Write solution set

The solution set of the inequality contains all real numbers less than 7

As, 7 is not included in the set so parentheses is used with it also $-\infty$ is not included so parentheses is used with it.

In interval form solution set is $\left(-\infty ,7\right)$

- Graph the solution set

Assolution set of the inequality is all real numbers less than 7

So arrow is towards $-\infty$ and open circle on 7 shows it is not included in the solution set.