Question

rewrite this as a 7th grader 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 \( \frac{1}{3}(6 - 12y) + \frac{1}{4}(24y + 14) \), we first need to distribute \( \frac{1}{3} \) to \( (6 - 12y) \) and \( \frac{1}{4} \) to \( (24y + 14) \).

1. **Distributing \( \frac{1}{3} \)**:
- \( \frac{1}{3} \times 6 = 2 \)
- \( \frac{1}{3} \times -12y = -4y \)

So, \( \frac{1}{3}(6 - 12y) \) becomes \( 2 - 4y \).

2. **Distributing \( \frac{1}{4} \)**:
- \( \frac{1}{4} \times 24y = 6y \)
- \( \frac{1}{4} \times 14 = \frac{7}{2} \)

So, \( \frac{1}{4}(24y + 14) \) becomes \( 6y + \frac{7}{2} \).

Now, we put both parts together:
\[ 2 - 4y + 6y + \frac{7}{2} \]

Next, we combine the like terms:
- For the \( y \) terms: \( -4y + 6y \) gives us \( 2y \).
- For the constant terms: \( 2 + \frac{7}{2} \).

To combine \( 2 \) and \( \frac{7}{2} \), we can change \( 2 \) into a fraction that has the same denominator as \( \frac{7}{2} \). This means turning \( 2 \) into \( \frac{4}{2} \).

So, now we have:
\[ \frac{4}{2} + \frac{7}{2} = \frac{11}{2} \]

Putting it all together, the simplified expression is:
\[ 2y + \frac{11}{2} \]