Question

Graph the solution set for the inequality$\mathbf{3}\mathit{x}\mathbf{-}\mathbf{6}\mathbf{\le }\mathbf{4}\mathit{x}\mathbf{-}\mathbf{4}\mathbf{\le }\mathbf{3}\mathit{x}\mathbf{+}\mathbf{1}$

Short answer

The graph of the solution set for the inequality $3x-6\le 4x-4\le 3x+1$is:

Step-by-step solution

Step1. Given

$3x-6\le 4x-4\le 3x+1$

$3x-6\le 4x-4\le 3x+1$

Step2. Solve the inequality.

Solve the inequality $3x-6\le 4x-4\le 3x+1$

$\begin{array}{c}3x-6\le 4x-4\le 3x+1\\ 3x-6+4\le 4x-4+4\le 3x+1+4\\ 3x-2\le 4x\le 3x+5\\ 3x-2-3x\le 4x-3x\le 3x+5-3x\\ 3x-3x-2\le x\le 3x-3x+5\\ -2\le x\le 5\\ x\in \left[-2,5\right]\end{array}$

Therefore, the solution set for the inequality $3x-6\le 4x-4\le 3x+1$is $x\in \left[-2,5\right]$

Step3. Graph the solution set for the inequality 3x−6≤4x−4≤3x+1

The solution set for the inequality $3x-6\le 4x-4\le 3x+1$is $x\in \left[-2,5\right]$. Therefore, the graph of the solution set for the inequality $3x-6\le 4x-4\le 3x+1$is: