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

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