Question

Solve$\left|3x-4\right|\ge 2.$Graph the solution and write the solution in internal notation .

Short answer

The required solution is$(-\infty ,\frac{2}{3}]\cup [2,\infty )$

Step-by-step solution

Given information

$\left|3x-4\right|\ge 2$

Calculation

$$\begin{gathered} \left|3x-4\right|\ge 2 \\ \Rightarrow -2\ge 3x-4\ge 2 \\ \Rightarrow -2+4\ge 3x\ge 2+4 \\ \Rightarrow 2\ge 3x\ge 6 \\ \Rightarrow \frac{2}{3}\ge x\ge \frac{6}{3} \\ \Rightarrow \frac{2}{3}\ge x\ge 2 \end{gathered}$$

The solution in interval notation is$(-\infty ,\frac{2}{3}]\cup [2,\infty )$

Graph the solution

Graph is