Question

Rewrite the expression without using the absolute value symbol.
\(\displaystyle{\left|{{3}{x}-{5}}\right|}\) if \(\displaystyle{x}\ge\frac{{5}}{{3}}\)

Answer 1

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 \(\displaystyle{\left|{{3}{x}-{5}}\right|}={3}{x}-{5}\).