Question

For the following exercises, solve the inequality and express the solution using interval notation.

Answer 1

Answer:

In interval notation, the solution of |3 x-2|<7 is $-\frac{5}{3} < x < 3$ or $\left\{-\frac{5}{3}, 3\right\}$.

Step-by-step explanation:

The given absolute value function is |3 x-2|<7.

It is required to solve the inequality and express the solution using interval notation. -B<x-A<B and solving them separately for x

Step 1 of 3

Given absolute value equation is |3 x-2|<7.

It can be written as -7<3 x-2<7.

To solve for the equality, 3x-2=7 and

$3 x-2=-7$

First, solve the equation 3x-2=7, then add 2 on both sides.

$\begin{aligned}&3 x=7+2 \\&3 x=9\end{aligned}$

Step 2 of 3

Simplify 3x=9 further, by dividing each side with 3 .

$\begin{aligned}&\frac{3 x}{3}=\frac{9}{3} \\&x=3\end{aligned}$

Step 3 of 3

Similarly, 3x-2=-7

From the above term 3x-2=-7,

Add 2 on each side.

$\begin{aligned}&3 x=-7+2 \\&3 x=-5\end{aligned}$

Simplify $3 x=-5$ further, by dividing each side with 3 .

$\begin{aligned}&\frac{3 x}{3}=-\frac{5}{3} \\&x=-\frac{5}{3}\end{aligned}$

Therefore, the solution is $-\frac{5}{3} < x < 3$ or $\left\{-\frac{5}{3}, 3\right\}$