Question

rewrite this

To simplify 1/3(6-12y)+1/4(24y+14) first distribute 1/3 to (6-12y) and 1/4 to (24y+14) then we combine the results. 2-4y+6y+7/2, then we combine like terms -4y+6y+2y. Combine 2 and 7/2, turn 2 into a fraction. put it all together and now the simplified expression is 2y+11/2

Answer 1

To simplify the expression \( \frac{1}{3}(6 - 12y) + \frac{1}{4}(24y + 14) \), start by distributing \( \frac{1}{3} \) to \( (6 - 12y) \) and \( \frac{1}{4} \) to \( (24y + 14) \). This gives us:

\[
\frac{1}{3} \cdot 6 - \frac{1}{3} \cdot 12y + \frac{1}{4} \cdot 24y + \frac{1}{4} \cdot 14
\]

Which simplifies to:

\[
2 - 4y + 6y + \frac{7}{2}
\]

Next, combine like terms. The \( y \) terms \( -4y + 6y \) combine to give \( 2y \). For the constant terms, we combine \( 2 \) and \( \frac{7}{2} \). To do this, we can convert \( 2 \) into a fraction:

\[
2 = \frac{4}{2}
\]

Now, adding \( \frac{4}{2} + \frac{7}{2} \) results in:

\[
\frac{11}{2}
\]

Putting it all together, the simplified expression is:

\[
2y + \frac{11}{2}
\]