Question

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

$2(3x-1)<4or3x-5>1$

Short answer

Solution of inequalities

$x<1orx>2$

Graph of solution of inequalities

The solution in interval notation.

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

Step-by-step solution

Step 1. Given information 

Consider the inequality

$2(3x-1)<4or3x-5>1$

Step 2. Solve each inequality

$$\begin{gathered} 2(3x-1)<4 \\ 3x-1<\frac{4}{2} \\ 3x-1<2 \\ 3x<2+1 \\ 3x<3 \\ x<\frac{3}{3} \\ x<1 \end{gathered}$$or$$\begin{gathered} 3x-5>1 \\ 3x>1+5 \\ 3x>6 \\ x>\frac{6}{3} \\ x>2 \end{gathered}$$

Step 3. Graph each inequality  

For$x<1$

For$x>2$

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

The solution in interval notation

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