Given the equation:
[tex]-7=\frac{3y+7}{4}-\frac{9y-5}{2}[/tex]
We will solve the equation to find y
Multiply the equation by 4 to eliminate the denominators
[tex]\begin{gathered} 4(-7)=4\cdot\frac{3y+7}{4}-4\cdot\frac{9y-5}{2} \\ \\ -28=(3y+7)-2(9y-5) \\ -28=3y+7-18y+10 \end{gathered}[/tex]
Combine the like terms
[tex]\begin{gathered} -28=(3y-18y)+(7+10) \\ -28=-15y+17 \\ \end{gathered}[/tex]
Subtract (17) to both sides
[tex]\begin{gathered} -28-17=-15y+17-17 \\ -45=-15y \end{gathered}[/tex]
Divide both sides by (-15)
[tex]\begin{gathered} \frac{-45}{-15}=\frac{-15y}{-15} \\ \\ y=3 \end{gathered}[/tex]
So, the answer will be y = 3
