Answer :
Given the equation:
[tex]\frac{y+10}{11}-\frac{5-y}{22}=5[/tex]we will find the value of y as follows:
1) Multiply all terms by 22
[tex]\begin{gathered} 22\cdot\frac{(y+10)}{11}-22\cdot\frac{(5-y)}{22}=22\cdot5 \\ 2(y+10)-(5-y)=110 \end{gathered}[/tex]2) simplify and combine the like terms
[tex]\begin{gathered} 2y+20-5+y=110 \\ 3y+15=110 \end{gathered}[/tex]3) Subtract 15 from both sides
[tex]\begin{gathered} 3y+15-15=110-15 \\ 3y=95 \end{gathered}[/tex]4) Divide both sides by 3
[tex]\begin{gathered} \frac{3y}{3}=\frac{95}{3} \\ \\ y=\frac{95}{3}=31\frac{2}{3} \end{gathered}[/tex]