Question

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

$4-7x\ge -3or5(x-3)+8>3$

Short answer

Solution of inequalities

$x\le 1orx>2$

Graph of solution of inequalities

The solution in interval notation

$(-\infty ,1]\cup (2,\infty )$

Step-by-step solution

Step 1. Given information 

Consider each inequality

$4-7x\ge -3or5(x-3)+8>3$

Step 2. Solve each inequality 

$$\begin{gathered} 4-7x\ge -3 \\ -7x\ge -3-4 \\ -7x\ge -7 \\ x\le \frac{-7}{-7} \\ x\le 1 \end{gathered}$$or$$\begin{gathered} 5(x-3)+8>3 \\ 5(x-3)>3-8 \\ 5(x-3)>-5 \\ x-3>\frac{-5}{5} \\ x-3>-1 \\ x>-1+3 \\ x>2 \end{gathered}$$

Step 3. Graph each inequality 

For$x\le 1$

For$x>2$

Step 4. Graph number that make either one inequality true x≤1 or x>2

The solution in interval notation

$(-\infty ,1]\cup (2,\infty )$