Chapter 4, Problem 1RE

In Exercises 1 – 6, solve each linear inequality. Other than ø, graph the solution set on a number line.

$-6x+3\le 15$

To determine

To calculate: The solution set of the inequality $-6x+3\le 15$ and graph it on a number line.

Answer to Problem 1RE

Solution:

The solution set of the inequality $-6x+3\le 15$ is $\left[-2,\infty \right)$.

Explanation of Solution

Given:

The inequality $-6x+3\le 15$.

Calculation:

Consider the inequality:

$-6x+3\le 15$

Subtract 3 from both sides of the inequality to get:

$\begin{array}{c}-6x-3+3\le 15-3\\ -6x\le 12\end{array}$

Divide the inequality by 6 and change the sense of inequality to get:

$x\ge -2$

Hence,

The solution set of $-6x+3\le 15$ is $\left[-2,\infty \right)$.

Graph:

The solution set of $-6x+3\le 15$ is $\left[-2,\infty \right)$.

Therefore, the graph of the solution set on the number line is shown below: