Question

Simplify the expressions. 3/2 − 1/2 a+ 2/3 a+ 3/2

Answer 1

`(a)/(6)+3`

Explanation:

We have been given an expression and we are asked to simplify our given expression.

`(3)/(2) -(1)/(2)a+ (2)/(3) a+(3)/(2)`

First of all let us combine like terms.

`((2)/(3) -(1)/(2))a+((3)/(2)+(3)/(2))`

Now let us have a common denominator for the constant terms of a.

`((2*2)/(3*2) -(1*3)/(2*3))a+((3)/(2)+(3)/(2))`

`((4)/(6) -(3)/(6))a+((3)/(2)+(3)/(2))`

Now let us simplify the numerators.

`((4-3)/(6))a+((3+3)/(2))`

`((1)/(6))a+((6)/(2))`

Let us divide 6 by 2.

`(1)/(6)a+3`

`(a)/(6)+3`

Therefore, our expression simplifies to
`(a)/(6)+3`.