Question

Solve each inequality. Graph the solution set on a number line.

36. $\left|-5y\right|<35$

Short answer

Solution of inequality is $7>y\text{and}y>-7$

Solution set in number line is

Step-by-step solution

- Definition of absolute value inequality

For real numbers $a\text{and}b$ with $b>0$

Absolute value inequality is $\left|a\right|<b$ when $-b<a\text{and}a<b$, and

Absolute value inequality is $\left|a\right|>b$ when $a<-b\text{or}a>b$

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify -5y<35

From definition of absolute value inequality, given expression is simplified to

$-35<-5y\text{and}-5y<35$

Use division property of inequality, divide with same negative number reverse the sign of inequality as shown below

$\begin{array}{c}\frac{-35}{-5}>\frac{-5y}{-5}\text{and}\frac{-5y}{-5}>\frac{35}{-5}\\ 7>y\text{andy}>-7\end{array}$

- Graph the solution set

For $7>y\text{and}y>-7$, number line starts from $-7$ to 7

Open circle on $-7\text{and 7}$ shows these points are not included in the solution.