Question

Solve each equation. Match the solution with the correct equation. Some answer choices may be unneeded.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
2x - 6 = 24
2x + 6 = 24
2(x + 6) = 24
2(x - 6) = 24

Answer 1

Let's solve each equation step-by-step and find the solutions.

1. **Equation:** \( 2x - 6 = 24 \)

- Add 6 to both sides:
\[
2x = 30
\]
- Divide by 2:
\[
x = 15
\]

2. **Equation:** \( 2x + 6 = 24 \)

- Subtract 6 from both sides:
\[
2x = 18
\]
- Divide by 2:
\[
x = 9
\]

3. **Equation:** \( 2(x + 6) = 24 \)

- Divide by 2:
\[
x + 6 = 12
\]
- Subtract 6 from both sides:
\[
x = 6
\]

4. **Equation:** \( 2(x - 6) = 24 \)

- Divide by 2:
\[
x - 6 = 12
\]
- Add 6 to both sides:
\[
x = 18
\]

Now, let's summarize the solutions for each equation:

- For \( 2x - 6 = 24 \), the solution is \( x = 15 \).
- For \( 2x + 6 = 24 \), the solution is \( x = 9 \).
- For \( 2(x + 6) = 24 \), the solution is \( x = 6 \).
- For \( 2(x - 6) = 24 \), the solution is \( x = 18 \).

So the final results and their corresponding equations are:
- \( 2x - 6 = 24 \) → \( x = 15 \)
- \( 2x + 6 = 24 \) → \( x = 9 \)
- \( 2(x + 6) = 24 \) → \( x = 6 \)
- \( 2(x - 6) = 24 \) → \( x = 18 \)

Match them accordingly with the input sections.