Q8. - Algebra 2

Question

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

8. $2w+19<5$

Step-by-Step Solution

Answer

Solution of inequality $2w+19<5$ is $w<-7$

In set-builder form, solution set is $\left\{w|w<-7\right\}$

Solution set on number line is 

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify 2 w + 19 &#60; 5

To simplify given inequality, use subtraction and division property of inequalities. Subtract same number from both sides does not change inequality. Also divide by same positive number does not change the sign of inequality as shown below

$\begin{array}{c}2w+19<5\\ 2w+19-19<5-19\\ 2w<-14\\ \frac{2w}{2}<-\frac{14}{2}\\ w<-7\end{array}$

Step 3 - Write solution set

The solution set of the inequality $w<-7$ contains all real numbers less than $-7$

In set-builder form 

Solution set is $\left\{w|w<-7\right\}$

Step 4 - Graph the solution set

As solution set of the inequality $w<-7$ contains all real numbers less than $-7$

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