Question

Determine whether the following expressions are equivalent:

94a+28
and 108a−14(a−2)
.

(1 point)
Responses

Yes, because 108a−14(a−2)
simplifies to 94a+28
.
Yes, because 108 a minus 14 left parenthesis a minus 2 right parenthesis simplifies to 94 a plus 28 .

No, because 108a−14(a−2)
simplifies to 94a−28
.
No, because 108 a minus 14 left parenthesis a minus 2 right parenthesis simplifies to 94 a minus 28 .

No, because 108a−14(a−2)
simplifies to 136a−14
.
No, because 108 a minus 14 left parenthesis a minus 2 right parenthesis simplifies to 136 a minus 14 .

Yes, because 108a−14(a−2)
simplifies to 28−94a
.

Answer 1

To determine whether the expressions \( 94a + 28 \) and \( 108a - 14(a - 2) \) are equivalent, we need to simplify the second expression:

1. Start with \( 108a - 14(a - 2) \).
2. Distribute \( -14 \) in the second term:
\[
-14(a - 2) = -14a + 28
\]
3. Substitute this back into the expression:
\[
108a - 14a + 28
\]
4. Combine like terms:
\[
(108a - 14a) + 28 = 94a + 28
\]

Now we have simplified \( 108a - 14(a - 2) \) to \( 94a + 28 \).

Since both expressions are \( 94a + 28 \), they are indeed equivalent.

Therefore, the correct response is:
**Yes, because \( 108a - 14(a - 2) \) simplifies to \( 94a + 28 \).**