Question

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

$\frac{1}{2}x-5\le 3or\frac{1}{4}(x-8)\ge -3$

Short answer

Solution of inequalities

$x\le 16orx\ge -4$

Graph of solution of inequalities

The solution in interval notation

$(-\infty ,\infty )$

Step-by-step solution

Step 1. Given information 

Consider each inequality

$\frac{1}{2}x-5\le 3or\frac{1}{4}(x-8)\ge -3$

Step 2. Solve each inequality 

$$\begin{gathered} \frac{1}{2}x-5\le 3 \\ \frac{1}{2}x\le 3+5 \\ \frac{1}{2}x\le 8 \\ x\le 8\times 2 \\ x\le 16 \end{gathered}$$or$$\begin{gathered} \frac{1}{4}(x-8)\ge -3 \\ x-8\ge -3\times 4 \\ x-8\ge -12 \\ x\ge -12+8 \\ x\ge -4 \end{gathered}$$

Step 3. Graph each inequality 

For $x\le 16$

For$x\ge -4$

Step 4. Graph number that make either one inequality true x≤16 or x≥-4

The solution in interval notation

$(-\infty ,16]\cup [-4,\infty )=(-\infty ,\infty )$