Question

Solve each inequality, graph the solution, and write the solution in interval notation.

$3x+7\le 1and2x+3\ge -5$

Short answer

Solution of inequalities

$x\le -2andx\ge -4$

Graph of solution of inequalities

The solution in interval notation

$[-4,-2]$

Step-by-step solution

Step 1. Given information  

Consider each inequality

$3x+7\le 1and2x+3\ge -5$

Step 2. Solve each inequality 

$$\begin{gathered} 3x+7\le 1 \\ 3x\le 1-7 \\ 3x\le -6 \\ x\le \frac{-6}{3} \\ x\le -2 \end{gathered}$$and$$\begin{gathered} 2x+3\ge -5 \\ 2x\ge -5-3 \\ 2x\ge -8 \\ x\ge \frac{-8}{2} \\ x\ge -4 \end{gathered}$$

Step 3. Graph each inequality 

For$x\le -2$

For$x\ge -4$

Step 4. Graph number that make both inequality true. x≤-2 and x≥-4

The solution in interval notation

$[-4,-2]$