Question

solve the equation for y.
\\(\frac{13}{8}y + 3 - \frac{3}{4}y = \frac{5}{8}(2y - 12)\\)
a \\(y = 12\\)
b \\(y = 16.8\\)
c \\(y = 26\\)
d \\(y = 28\\)

Explanation:

Step1: Simplify both sides

First, simplify the left - hand side (LHS) and right - hand side (RHS) of the equation.
For the LHS: \(\frac{13}{8}y-\frac{3}{4}y + 3\). Since \(\frac{3}{4}y=\frac{6}{8}y\), then \(\frac{13}{8}y-\frac{6}{8}y+3=\frac{13 - 6}{8}y+3=\frac{7}{8}y + 3\).
For the RHS: \(\frac{5}{8}(2y-12)=\frac{5}{8}\times2y-\frac{5}{8}\times12=\frac{10}{8}y-\frac{60}{8}=\frac{5}{4}y-\frac{15}{2}\).
So the equation becomes \(\frac{7}{8}y + 3=\frac{5}{4}y-\frac{15}{2}\).

Step2: Eliminate fractions

Multiply every term in the equation by 8 (the least common multiple of 8 and 4 and 2) to get rid of the fractions.
\(8\times\frac{7}{8}y+8\times3 = 8\times\frac{5}{4}y-8\times\frac{15}{2}\)
Simplify each term:
\(7y + 24=10y-60\)

Step3: Solve for y

Subtract \(7y\) from both sides:
\(7y - 7y+24=10y - 7y-60\)
\(24 = 3y-60\)
Add 60 to both sides:
\(24 + 60=3y-60 + 60\)
\(84 = 3y\)
Divide both sides by 3:
\(y=\frac{84}{3}=28\)

Answer:

D. \(y = 28\)