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

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 .

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

1 answer

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

Starting with the expression \( 108a - 14(a - 2) \):

  1. Distribute \( -14 \) into \( (a - 2) \): \[ -14(a - 2) = -14a + 28 \]

  2. Now substitute this back into the expression: \[ 108a - 14a + 28 \]

  3. Combine like terms: \[ 108a - 14a = 94a \] Therefore, \[ 108a - 14(a - 2) = 94a + 28 \]

Since we simplified \( 108a - 14(a - 2) \) to \( 94a + 28 \), we can conclude that the two expressions are equivalent.

Thus, the correct response is:

Yes, because \( 108a - 14(a - 2) \) simplifies to \( 94a + 28 \).