Answer:
y = 11/29 = 0.38
Step-by-step explanation:
We have:
[tex]\frac{1}{3}y+\frac{1}{5}=2y+\frac{1}{11}y-\frac{7}{15}[/tex]To solve this question, we have to find the least common multiple, which is 11*15 = 165.
To find the least common number, we have to factor the denominators together:
3, 5, 11, 15 | 3
1, 5, 11, 5 | 5
1, 1, 11, 1 | 11
1, 1, 1, 1
The least common multiple is 3*5*11 = 165.
[tex]\begin{gathered} \frac{1}{3}y+\frac{1}{5}=2y+\frac{1}{11}y-\frac{7}{15} \\ \frac{55y+33=165\cdot2y+15y-77}{165} \\ 55y+33=330y+15y-77 \\ 55y-330y-15y=-77-33 \\ -290y=-110 \\ y=\frac{-110}{-290} \\ y=\frac{11}{29}=0.38 \end{gathered}[/tex]