Question

Could you please show me how to solve for x.
(2)/(3)(y+2)-(5)/(6)(y-1)=(5)/(4)(y-3)-4

Answer 1

\[\frac{2}{3}(y+2)-\frac{5}{6}(y-1)= \frac{5}{4}(y-3)-4\]right?

Answer 2

The most convenient thing to do first would be to get rid of the fractions by multiplying the whole equation by 12, which is the least common multiple of all of the denominators:

3 6 9 12 15
6 12 18
4 8 12 16

As you can see, 12 is the first number that appears in each row. After we do that multiplication, we have:
\[12*\frac{2}{3}(y+2)-12*\frac{5}{6}(y-1)= 12*\frac{5}{4}(y-3)-12*4\]\[8(y+2) - 10(y-1)=15(y-3)-48\]Apply the distributive property of multiplication, then solve for \(y\).