Question

which expression is equivalent to \\(\left(\frac{1}{4}y + 5\
ight) + \left(\frac{1}{2}y - 2\
ight)\\)? \\(\frac{3}{4}y + 3\\) \\(\frac{3}{4}y + 7\\) \\(\frac{1}{6}y + 3\\) \\(\frac{1}{6}y + 7\\)

Explanation:

Step1: Remove parentheses

We can remove the parentheses since there's addition, so the expression becomes $\frac{1}{4}y + 5 + \frac{1}{2}y - 2$.

Step2: Combine like terms for y

Find a common denominator for the y - terms. The common denominator of 4 and 2 is 4. So $\frac{1}{2}y=\frac{2}{4}y$. Then $\frac{1}{4}y+\frac{2}{4}y=\frac{1 + 2}{4}y=\frac{3}{4}y$.

Step3: Combine constant terms

$5-2 = 3$.

Step4: Combine results

Putting the combined y - term and the combined constant term together, we get $\frac{3}{4}y+3$.

Answer:

$\frac{3}{4}y + 3$ (the first option among the given choices)