Q14. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

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 3 x − 6 ≤ 4 x − 4 ≤ 3 x + 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: