Question

# Rewrite the expression without using the absolute value symbol. abs(3x-5) if x>= 5/3

Piecewise-Defined Functions
Rewrite the expression without using the absolute value symbol.
$$\displaystyle{\left|{{3}{x}-{5}}\right|}$$ if $$\displaystyle{x}\ge\frac{{5}}{{3}}$$

2021-03-08
Step 1
The expression inside the absolute value is (3x-5).
The absolute value of a number, a, is equal to the distance that 'a' is from zero.
$$\displaystyle{\left|{{a}}\right|}={a},{\quad\text{if}\quad}{a}\ge{0}$$
=-(a), if a < 0
In the original definition for absolute value, replace each occurrence of 'a' with (3x-5).
$$\displaystyle{\left|{{3}{x}-{5}}\right|}={3}{x}-{5}$$, if $$\displaystyle{3}{x}-{5}\ge{0}$$
=-(3x-5), if 3x-5
Step 2
if $$\displaystyle{x}\ge\frac{{5}}{{3}}$$, then $$\displaystyle{\left|{{3}{x}-{5}}\right|}={3}{x}-{5}$$.