Answer:
-2 ≤ x ≤ 5
Explanation:
Given the compound inequalities:
[tex]4x-6\le14\text{ and 3}x+5\ge-1[/tex]
First, solve each of the inequalities separately:
[tex]\begin{gathered} 4x-6\le14 \\ \text{Add 6 to both sides} \\ 4x-6+6\le14+6 \\ 4x\le20 \\ \text{Divide both sides by 4} \\ \frac{4x}{4}\le\frac{20}{4} \\ x\le5 \end{gathered}[/tex]
Similarly, solve the second one:
[tex]\begin{gathered} 3x+5\ge-1 \\ \text{Add -5 to both sides} \\ 3x+5-5\ge-1-5 \\ 3x\ge-6 \\ \text{Divide both sides by }3 \\ \frac{3x}{3}\ge-\frac{6}{3} \\ x\ge-2 \\ \implies-2\le x \end{gathered}[/tex]
The solution to the compound inequality is:
[tex]-2\le x\le5[/tex]
The graph of the solution is attached below:
