Q36. - Algebra 2

Question

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

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

Step-by-Step Solution

Answer

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

Solution set in number line is

Step 1 - 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 $a<-b\text{ or }a>b$

Step 2 - Write properties of inequality

Properties of inequalities are written in following table:

Step 3 - Simplify - 5 y &#60; 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

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

Step 3 - 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.