Question

solve for all values of x in simplest form. 4 + 3|3x - 7| = 28

Explanation:

Step1: Isolate the absolute value term

Subtract 4 from both sides of the equation \(4 + 3|3x - 7| = 28\).
\(3|3x - 7| = 28 - 4\)
\(3|3x - 7| = 24\)

Step2: Solve for the absolute value

Divide both sides by 3.
\(|3x - 7| = \frac{24}{3}\)
\(|3x - 7| = 8\)

Step3: Consider the two cases for absolute value

Case 1: \(3x - 7 = 8\)
Add 7 to both sides: \(3x = 8 + 7\)
\(3x = 15\)
Divide by 3: \(x = \frac{15}{3}\)
\(x = 5\)

Case 2: \(3x - 7 = -8\)
Add 7 to both sides: \(3x = -8 + 7\)
\(3x = -1\)
Divide by 3: \(x = -\frac{1}{3}\)

Answer:

\(x = 5\) or \(x = -\frac{1}{3}\)