Question

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

$6(2x-1)>6and5(x+2)\ge 0$

Short answer

Solution of inequalities

$x>1andx\ge -2$

Graph of solution of inequalities

The solution in interval notation

$(1,\infty )$

Step-by-step solution

Step 1. Given information 

Consider each inequality

$6(2x-1)>6and5(x+2)\ge 0$

Step 2. Solve each inequality 

$$\begin{gathered} 6(2x-1)>6 \\ 2x-1>\frac{6}{6} \\ 2x-1>1 \\ 2x>1+1 \\ 2x>2 \\ x>\frac{2}{2} \\ x>1 \end{gathered}$$and$$\begin{gathered} 5(x+2)\ge 0 \\ x+2\ge \frac{0}{5} \\ x+2\ge 0 \\ x\ge 0-2 \\ x\ge -2 \end{gathered}$$

Step 3. Graph each inequality  

For$x>1$

For$x\ge -2$

Step 4. Graph number that make both inequality true. x>1 and x≥-2

The solution in interval notation

$(1,\infty )$