Chapter 8, Problem 43CR

To determine

Solve the inequality $a-15\le 3$ and graph the solution on number line

Answer to Problem 43CR

  $a\le 18$

Explanation of Solution

Given:

The inequality, $a-15\le 3$

Concept used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• Inequality sign get reverse on multiplying or dividing by a negative number

Calculation:

In order to solve the mixed inequality $a-15\le 3$ first isolate the variable term x by performing some basic operations. Here to isolate x terms on the left side, first add both sides by $15$ and then simplify further as shown below:

  $\begin{array}{l}a-15\le 3\\ a-15+15\le 3+15\\ a\le 18\end{array}$

Thus, the solution of the given inequality is $a\le 18$ .

The graph of the inequality solution $a\le 18$ is below: