91Ó°ÊÓ

Absolute value describes the distance from zero that a number is on the number line,without considering direction. The absolute value of a number is never negative.

Consider the expression $|3x-7|-5=-3$.

Add 5 on both sides of the equation as follows:

$\begin{array}{l}|3x−7|−5=−3\\ |3x−7|−5+5=−3+5\\ |3x−7|=2\end{array}$

Apply the absolute rule as follows:

Case 1. When $3x-7=-2$.

$\begin{array}{l}3x−7=−2\\ 3x−7+2=0\\ 3x−5=0\\ 3x=5\\ x=\frac{5}{3}\end{array}$

Case 2. When $3x-7=2$

$\begin{array}{l}3x−7=2\\ 3x−7−2=0\\ 3x−9=0\\ 3x=9\\ x=3\end{array}$

Therefore, the value is$x=3,\frac{5}{3}$.

Substitute $x=3,\frac{5}{3}$in the equation $|3x-7|-5=-3$and simplify as follows:

$\begin{array}{l}|3x−7|−5=−3\\ |3\left(3\right)−7|−5=−3\\ |9−7|−5=−3\\ \left|2\right|−5=−3\\ 2−5=−3\\ −3=−3\end{array}$

$\begin{array}{l}|3x−7|−5=−3\\ |3\left(\frac{5}{3}\right)−7|−5=−3\\ |5−7|−5=−3\\ |−2|−5=−3\\ 2−5=−3\\ −3=−3\end{array}$

Since the left-hand side and right-hand side is equal in both the cases thus the values are $x=3,\frac{5}{3}$.