Respuesta :
Answer:
In interval notation, the solution of |3 x-2|<7 is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex].
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
[tex]$3 x-2=-7$[/tex]
First, solve the equation 3x-2=7, then add 2 on both sides.
[tex]$\begin{aligned}&3 x=7+2 \\&3 x=9\end{aligned}$[/tex]
Step 2 of 3
Simplify 3x=9 further, by dividing each side with 3 .
[tex]$\begin{aligned}&\frac{3 x}{3}=\frac{9}{3} \\&x=3\end{aligned}$[/tex]
Step 3 of 3
Similarly, 3x-2=-7
From the above term 3x-2=-7,
Add 2 on each side.
[tex]$\begin{aligned}&3 x=-7+2 \\&3 x=-5\end{aligned}$[/tex]
Simplify $3 x=-5$ further, by dividing each side with 3 .
[tex]$\begin{aligned}&\frac{3 x}{3}=-\frac{5}{3} \\&x=-\frac{5}{3}\end{aligned}$[/tex]
Therefore, the solution is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex]
