Question

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

$4-3x\le -2or2x-1\le -5$

Short answer

Solution of inequalities

$x\ge 2orx\le -2$

Graph of solution of inequalities

The solution in interval notation.

$(-\infty ,-2]\cup [2,\infty )$

Step-by-step solution

Step 1. Given information 

Consider the inequality

$4-3x\le -2or2x-1\le -5$

Step 2. Solve each inequality 

$$\begin{gathered} 4-3x\le -2 \\ -3x\le -2-4 \\ -3x\le -6 \\ x\ge \frac{-6}{-3} \\ x\ge 2 \end{gathered}$$orrole="math" localid="1644727585170" $$\begin{gathered} 2x-1\le -5 \\ 2x\le -5+1 \\ 2x\le -4 \\ x\le \frac{-4}{2} \\ x\le -2 \end{gathered}$$

Step 3. Graph each inequality 

For$x\ge 2$

For$x\le -2$

Step 4. Graph number that make either one inequality true x≥2 or x≤-2

The solution in interval notation.

$(-\infty ,-2]\cup [2,\infty )$