Question

solve: |3x - 5| = 4
a. {-3, -1/3}
b. {-1/3, -3}
c. {3, 1/3}
d. {1/3, -1/3}

Explanation:

Step1: Split absolute value equation

An absolute value equation \(|A| = B\) splits into \(A = B\) and \(A = -B\). So:
\(3x - 5 = 4\) and \(3x - 5 = -4\)

Step2: Solve first equation

Isolate \(x\) for \(3x - 5 = 4\):
Add 5 to both sides: \(3x = 4 + 5 = 9\)
Divide by 3: \(x = \frac{9}{3} = 3\)

Step3: Solve second equation

Isolate \(x\) for \(3x - 5 = -4\):
Add 5 to both sides: \(3x = -4 + 5 = 1\)
Divide by 3: \(x = \frac{1}{3}\)

Step4: Compile solution set

The solutions are \(3\) and \(\frac{1}{3}\), so the set is \(\{3, \frac{1}{3}\}\)

Answer:

C. {3, ¹/₃}