Question

solve for y.

$-\frac{3}{4}y+\frac{5}{3}=-6y - \frac{5}{4}$

simplify your answer as much as possible.

Explanation:

Step1: Move terms with y to one - side

Add \(6y\) to both sides of the equation:
\(-\frac{3}{4}y + 6y+\frac{5}{3}=-6y + 6y-\frac{5}{4}\)
\((-\frac{3}{4}+6)y+\frac{5}{3}=-\frac{5}{4}\)
\((-\frac{3}{4}+\frac{24}{4})y+\frac{5}{3}=-\frac{5}{4}\)
\(\frac{-3 + 24}{4}y+\frac{5}{3}=-\frac{5}{4}\)
\(\frac{21}{4}y+\frac{5}{3}=-\frac{5}{4}\)

Step2: Move the constant term to the other side

Subtract \(\frac{5}{3}\) from both sides:
\(\frac{21}{4}y+\frac{5}{3}-\frac{5}{3}=-\frac{5}{4}-\frac{5}{3}\)
\(\frac{21}{4}y=-\frac{5\times3}{4\times3}-\frac{5\times4}{3\times4}\)
\(\frac{21}{4}y=-\frac{15}{12}-\frac{20}{12}\)
\(\frac{21}{4}y=-\frac{15 + 20}{12}\)
\(\frac{21}{4}y=-\frac{35}{12}\)

Step3: Solve for y

Multiply both sides by \(\frac{4}{21}\):
\(y=-\frac{35}{12}\times\frac{4}{21}\)
\(y=-\frac{35\times4}{12\times21}\)
\(y =-\frac{140}{252}\)
Simplify the fraction: \(y=-\frac{5}{9}\)

Answer:

\(y =-\frac{5}{9}\)