Chapter 8, Problem 47CR

To determine

Solve the inequality $-5x<-13$ and graph the solution on number line

Answer to Problem 47CR

  $x>\frac{13}{5}$

The graph of the solution $x>\frac{13}{5}$ on number line is below:

  

Explanation of Solution

Given:

The inequality, $-5x<-13$

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 $-5x<-13$ first isolate the variable term x by performing some basic operations. Here to isolate x terms on the left side, first divide both sides by $-5$ and then Inequality sign get reverse on multiplying or dividing by a negative number and then simplify further as shown below:

  $\begin{array}{l}-5x<-13\\ \frac{-5x}{-5}<\frac{-13}{-5}\\ x>\frac{13}{5}\end{array}$

Thus, the solution of the given inequality is $x>\frac{13}{5}$ .

The graph of the inequality solution $x>\frac{13}{5}$ is below: