Which of the following describes the correct process for solving the equation 2x − 4 = 20 and arrives at the correct solution?

Add 4 to both sides, and then divide by 2. The solution is x = 12.
Divide both sides by −4, and then subtract 2. The solution is x = −7.
Subtract 4 from both sides, and then divide by 2. The solution is x = −12.
Multiply both sides by −4, and then divide by 2. The solution is x = −40.

Let's analyze each option to determine the correct process for solving the equation \(2x - 4 = 20\) and finding the correct solution.

### Step 1: Solve the equation
The equation is \(2x - 4 = 20\).

1. **Add 4 to both sides**:
   \[
   2x - 4 + 4 = 20 + 4
   \]
   This simplifies to:
   \[
   2x = 24
   \]

2. **Divide both sides by 2**:
   \[
   \frac{2x}{2} = \frac{24}{2}
   \]
   This simplifies to:
   \[
   x = 12
   \]

### Step 2: Evaluate each given process
1. **Add 4 to both sides, and then divide by 2. The solution is x = 12.**
   - This is the correct process and solution.

2. **Divide both sides by −4, and then subtract 2. The solution is x = −7.**
   - This process is incorrect. Dividing by \(-4\) does not simplify the equation correctly.

3. **Subtract 4 from both sides, and then divide by 2. The solution is x = −12.**
   - This process is incorrect. Subtracting 4 from both sides leads to the wrong result.

4. **Multiply both sides by −4, and then divide by 2. The solution is x = −40.**
   - This process is incorrect. Multiplying by \(-4\) and then dividing by 2 does not solve the equation correctly.

### Conclusion
The correct process is the first option: **Add 4 to both sides, and then divide by 2. The solution is \(x = 12\).**

Would you like more details or have any questions?

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Here are 5 related questions:
1. How would you solve the equation \(3x + 5 = 14\)?
2. What happens if you subtract 4 from both sides of the equation \(2x - 4 = 20\)?
3. Can you describe how to check if the solution \(x = 12\) is correct for the equation \(2x - 4 = 20\)?
4. What is the difference between adding and subtracting when solving an equation?
5. How do you solve an equation with a variable on both sides?

**Tip:** Always perform the same operation on both sides of an equation to maintain the equality.

Explore how to solve equations step-by-step with examples. This page discusses solving linear equations by performing operations on both sides. Suitable for students in Grades 6-8.

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