Chapter 8.8, Problem 66CCR

To determine

Solve the inequality $-13\ge x-8$ and graph the solution on number line

Answer to Problem 66CCR

The solution of the inequality is $x\le -5$

The graph of the solution $x\le -5$ on number line is below:

  

Explanation of Solution

Given:

The inequality, $-13\ge x-8$

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 $-13\ge x-8$ 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 $8$ and then simplify further as shown below:

  $\begin{array}{c}-13\ge x-8\\ -13+8\ge x-8+8\\ -5\ge x\\ \Rightarrow x\le -5\end{array}$

Thus, the solution of the given inequality is $x\le -5$ .

The graph of the inequality solution $x\le -5$ is below: