Question

solve.
separate your answers with a comma, and please write fractions in reduced form, no decimals.
$3|4x - 5| = 6$

Explanation:

Step1: Divide both sides by 3

To isolate the absolute - value expression, we divide both sides of the equation \(3|4x - 5|=6\) by 3.
\(\frac{3|4x - 5|}{3}=\frac{6}{3}\)
Simplifying, we get \(|4x - 5| = 2\)

Step2: Set up two cases

Case 1: The expression inside the absolute value is non - negative, so \(4x-5 = 2\)
Add 5 to both sides: \(4x=2 + 5\)
\(4x=7\)
Divide both sides by 4: \(x=\frac{7}{4}\)

Case 2: The expression inside the absolute value is negative, so \(4x - 5=-2\)
Add 5 to both sides: \(4x=-2 + 5\)
\(4x = 3\)
Divide both sides by 4: \(x=\frac{3}{4}\)

Answer:

\(\frac{3}{4},\frac{7}{4}\)