Question

Expand −1/4(6x+4)
.(1 point)
Responses

−64x−4
or −32x−4
negative Start Fraction 6 over 4 End Fraction x minus 4 or negative Start Fraction 3 over 2 End Fraction x minus 4

−624x−4
or −14x−4
negative Start Fraction 6 over 24 End Fraction x minus 4 or negative Start Fraction 1 over 4 End Fraction x minus 4

−624x−416
or −14x−14
negative Start Fraction 6 over 24 End Fraction x minus Start Fraction 4 over 16 End Fraction or negative Start Fraction 1 over 4 End Fraction x minus Start Fraction 1 over 4 End Fraction

−6/4x−4/4
or −3/2x−1

Answer 1

To expand the expression \(-\frac{1}{4}(6x + 4)\), we distribute \(-\frac{1}{4}\) to both terms inside the parentheses.

1. Distributing \(-\frac{1}{4}\) to \(6x\):
\[
-\frac{1}{4}(6x) = -\frac{6}{4}x = -\frac{3}{2}x
\]

2. Distributing \(-\frac{1}{4}\) to \(4\):
\[
-\frac{1}{4}(4) = -\frac{4}{4} = -1
\]

Now, combine the results:
\[
-\frac{3}{2}x - 1
\]

Thus, the expanded expression is:
\[
-\frac{3}{2}x - 1
\]

From the available responses, the correct one is:
\[-\frac{3}{2}x - 1\] or \( -\frac{6}{4}x - \frac{4}{4}\).