Question

solve the equation.
\\(\frac{1}{2}y - 3 = 7 - \frac{5}{4}y\\)

select the correct choice below and, if necessary, fill in the answer box to complete your choice

a. \\(y = \\) (type an integer or a simplified fraction )

b. the solution is all real numbers.

c. there is no solution.

Explanation:

Step1: Add $\frac{5}{4}y$ to both sides

To eliminate the $y$-term on the right, we add $\frac{5}{4}y$ to each side. This gives us $\frac{1}{2}y+\frac{5}{4}y - 3=7$. First, we need to find a common denominator for the $y$-terms. The common denominator of 2 and 4 is 4. So, $\frac{1}{2}y=\frac{2}{4}y$. Then $\frac{2}{4}y+\frac{5}{4}y=\frac{2 + 5}{4}y=\frac{7}{4}y$. So the equation becomes $\frac{7}{4}y-3 = 7$.

Step2: Add 3 to both sides

To isolate the term with $y$, we add 3 to both sides of the equation. So, $\frac{7}{4}y-3 + 3=7 + 3$, which simplifies to $\frac{7}{4}y=10$.

Step3: Solve for $y$

To solve for $y$, we multiply both sides of the equation by the reciprocal of $\frac{7}{4}$, which is $\frac{4}{7}$. So, $y = 10\times\frac{4}{7}=\frac{40}{7}$.

Answer:

A. $y=\frac{40}{7}$