Question

write an expression that is equivalent to 1/4a - 3.

1/4a - 3 =__ (a - __)

Answer 1

To rewrite the expression \( \frac{1}{4}a - 3 \) in the form \( (a - \_\_) \), we will factor out \( \frac{1}{4} \).

Start with the expression:

\[
\frac{1}{4}a - 3
\]

We want to factor out \( \frac{1}{4} \):

\[
\frac{1}{4}(a - \_\_)
\]

To find what goes in the blank, we need to set the inside of the parentheses equal to the original expression. We can rewrite \( -3 \) in a form that involves \( \frac{1}{4} \):

\[
-3 = -\frac{12}{4}
\]

So, the expression can be rewritten as:

\[
\frac{1}{4}(a - 12)
\]

Thus, the final equivalent expression is:

\[
\frac{1}{4}a - 3 = \frac{1}{4}(a - 12)
\]

In the format given, it can be stated as:

\[
\frac{1}{4}a - 3 = \frac{1}{4}(a - 12)
\]

So, filling in the blanks:

\[
\frac{1}{4}a - 3 = (a - 12)
\]

However, remember that \( \frac{1}{4} \) is factored out, so the expression we derived is correct as it stands. The final part you intended with \( \_\_ \) would be filled by noting that 12 is needed to balance the equation wrt the original expression's constants.