To solve the equation:

$|3x - 7| = 5$

we need to consider the definition of absolute value. This equation implies two possible cases, since $|A| = B$ means $A = B$ or $A = -B$.

Case 1: $3x - 7 = 5$

1. Add 7 to both sides: $3x = 12$

2. Divide by 3: $x = 4$

Case 2: $3x - 7 = -5$

1. Add 7 to both sides: $3x = 2$

2. Divide by 3: $x = \frac{2}{3}$

Solution

The two solutions are: $x = 4 \quad \text{and} \quad x = \frac{2}{3}$

Would you like more details on absolute value equations, or have any questions?

Here are 5 related questions:

1. How do you solve absolute value equations with more complex expressions?
2. What happens when an absolute value equation has no solutions?
3. How can absolute value inequalities be solved?
4. Can we use a graphical approach to solve absolute value equations?
5. How does adding or subtracting constants affect the solutions of absolute value equations?

Tip: Always check your solutions by plugging them back into the original equation, especially with absolute values.