Solve the Absolute Value Equation: |3x - 5| = 4

To solve this problem, we'll follow these steps:

• Step 1: Consider the positive scenario: $3x - 5 = 4$
• Step 2: Consider the negative scenario: $3x - 5 = -4$
• Step 3: Solve each equation separately
• Step 4: Identify the correct answer from the given choices

Let's work through each step:

Step 1: Solve $3x - 5 = 4$.
Add 5 to both sides: $3x - 5 + 5 = 4 + 5$
So, $3x = 9$.
Divide both sides by 3: $x = \frac{9}{3}$, thus $x = 3$.

Step 2: Solve $3x - 5 = -4$.
Add 5 to both sides: $3x - 5 + 5 = -4 + 5$
So, $3x = 1$.
Divide both sides by 3: $x = \frac{1}{3}$.

Step 3: We have two solutions for $x$, namely $x = 3$ and $x = \frac{1}{3}$.

Step 4: Comparing this with the given choices, the correct answer is "Answers b + c":

• $x = 3$ corresponds to choice b.
• $x = \frac{1}{3}$ corresponds to choice c.

Therefore, the solution to the problem is Answers b + c.