Question

Expanding and Adding Expressions Use the expansion shown to simplify the expression. One-half (3 x minus two-thirds y) + 3 (StartFraction x over 2 EndFraction + one-half y) Equals (one-half) (StartFraction 3 over 1 EndFraction x) + (one-half) (Negative two-thirds y) + (StartFraction 3 over 1 EndFraction) (one-half x) + (StartFraction 3 over 1 EndFraction) (one-half y) Equals (three-halves x) + (negative one-third y) + (three-halves x) + (three-halves y) = 3x + y

Answer 1

`3x+(7)/(6)y`

Explanation:

To simplify the expression, we first open the parenthesis, then we collect all the like terms. Lastly we simplify the like terms to its simplest form. Given that:

`(1)/(2)(3x-(2)/(3) y)+3((x)/(2)+(1)/(2)y )\\\\Firstly, we\ expand\ the\ parenthesis:\\\\=(1)/(2)(3x)-(1)/(2)((2)/(3) y)+3(x)/(2)+3((1)/(2) y)\\`

`=(3)/(2)x-(1)/(3)y +(3)/(2)x+(3)/(2) y\\\\ Collecting\ like\ terms:\\\\=(3)/(2)x+(3)/(2)x-(1)/(3)y+(3)/(2)y\\\\Adding \ terms:\\\\=3x +(7)/(6)y`