Question

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

71. |3x − 2 | < 7

Answer 1

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

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 .

`$$\begin{aligned}&(3 x)/(3)=(9)/(3) \\&x=3\end{aligned}$$`

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 .

`$$\begin{aligned}&(3 x)/(3)=-(5)/(3) \\&x=-(5)/(3)\end{aligned}$$`

Therefore, the solution is
`$-(5)/(3) < x < 3$` or
`$\left\{-(5)/(3), 3\right\}$`