Solve for the variable and check answer. A) `2/3x=1/15x+3/5` B) `2+y/2=3/4y-3`

A. `2/3x=1/15x + 3/5`

First, express the equation with whole numbers. To do so, multiply both sides by the LCD of the fractions which is 15.

`15*2/3x=(1/15x + 3/5)*15`

`15*2/3x=15*1/15x + 15*3/5`

`10x=x+9`

Then, bring together the terms with x. So, subtract both sides by x.

`10x-x=x-x+9`

`10x-x=9`

`9x=9`

Then, divide both sides by 9, to get x only at the left side of the equation.

`(9x)/9=9/9`

`x=1`

To check, plug-in the value of x to the original equation.

2/3x =1/15x + 3/5

2/3*1=1/15*1+3/5

2/3=1/15+3/5

The LCD of the fractions at the left is 15. So multiply 3/5 by 3/3 to have a denominator of 15.

2/3=1/15+3/5*3/3

2/3=1/15+9/15

Now that the right side have the same denominators, proceed to add.

2/3=10/15

Reduce the fraction to its lowest term.

2/3=2/3   (True)

Hence, the solution is x=1.

(For the second equation, please post it as separate question in Homework Help.)

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