To solve the absolute value equation $|2x - 3| = 7$, follow these steps:

Step 1: Split the absolute value equation

The absolute value equation $|A| = B$ implies two cases:

1. $A = B$
2. $A = -B$

For $|2x - 3| = 7$, we set up the two cases:

1. $2x - 3 = 7$
2. $2x - 3 = -7$

Step 2: Solve each equation

Case 1: $2x - 3 = 7$

Add 3 to both sides: $2x = 10$

Divide by 2: $x = 5$

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

Add 3 to both sides: $2x = -4$

Divide by 2: $x = -2$

Step 3: Combine the solutions

The solution to the equation $|2x - 3| = 7$ is: $x = 5 \quad \text{or} \quad x = -2$

Do you want a graphical explanation or further breakdown of these steps?

Here are 5 related questions to deepen your understanding:

1. How do you solve $|3x + 4| = 10$?
2. What are the steps to check if a solution satisfies the absolute value equation?
3. How do you solve equations with absolute values on both sides, like $|x + 2| = |3x - 1|$?
4. Can an absolute value equation have no solutions? If so, when?
5. How can you graph an absolute value equation and interpret its solutions?

Tip: Always check your solutions by substituting them back into the original equation to ensure they satisfy the absolute value condition!