Question

.
Which of the following equations is equivalent to 4(a + 2) – 2(a – 8) = 24?

2a + 24 = 24

2a - 8 = 24

6a - 8 = 24

6a + +24 = 24

Answer 1

To determine which equation is equivalent to the given equation \( 4(a + 2) - 2(a - 8) = 24 \), let's simplify the left-hand side step by step.

1. Distribute the \( 4 \) on the first term:
\[
4(a + 2) = 4a + 8
\]

2. Distribute the \( -2 \) on the second term:
\[
-2(a - 8) = -2a + 16
\]

3. Combine both results:
\[
4(a + 2) - 2(a - 8) = (4a + 8) + (-2a + 16) = 4a + 8 - 2a + 16
\]

4. Combine like terms:
\[
4a - 2a + 8 + 16 = 2a + 24
\]

Now, we have:
\[
2a + 24 = 24
\]

Thus, the equation \( 2a + 24 = 24 \) is equivalent to the original equation \( 4(a + 2) - 2(a - 8) = 24 \).

So, the correct answer is:
\[
\boxed{2a + 24 = 24}
\]