Q16. - Algebra 2

Question

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

16. $b-3\le 15$

Step-by-Step Solution

Answer

Solution of inequality $b-3\le 15$ is $b\le 18$

In interval form, solution set is $\left(-\infty ,18\right]$

Solution set on number line is 

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify b − 3 ≤ 15

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

$\begin{array}{c}b-3\le 15\\ b-3+3\le 15+3\\ b\le 18\end{array}$

Step 3 - Write solution set

The solution set of the inequality contains all real numbers less than or equal to 18

As, 18 is included in the set so bracket is used with it whereas $-\infty$ is not included so parentheses is used with it.

In interval form solution set is $\left(-\infty ,18\right]$

Step 4 - Graph the solution set

As solution set of the inequality is all real numbers less than or equal to 18

So arrow is towards $-\infty$ and dot on 18 shows it is included in the solution set.