Chapter 4, Problem 9CR

To determine

The solution of the inequality $3x+2\le 5x-1$ and graph the solution set

Answer to Problem 9CR

Solution:

The solution of the inequality is $\left[3/2,\infty \right)$ and the graph is

  

Explanation of Solution

Given information:

The inequality $3x+2\le 5x-1$

Rearrange the inequality, so that $0$ is on the right side

  $3x+2-5x+1\le 0$

  $\Rightarrow -2x+3\le 0$

  $\Rightarrow -2x\le -3$

  $\Rightarrow x\ge \frac{3}{2}$ .

Thus, the solution set of the inequality is $\left[3/2,\infty \right)$

Hence, the graph of the solution set is