Question

Determine whether the following expressions are equivalent: 94a+28 and 108a−14(a−2) . (1 point) Responses 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 . 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 . Skip to navigation

Answer 1

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

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

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

2. Substitute this back into the expression: \[ 108a - 14(a - 2) = 108a - 14a + 28 \]

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

Now we have: \[ 108a - 14(a - 2) = 94a + 28 \]

This shows that the two expressions are indeed equivalent.

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