Add 1/2(x+4)+1/4(4x-2)

Answer 1

1/2(x+4)+1/4(4x-2) can be simplified as follows:

1/2(x+4) + 1/4(4x-2)
= (1/2)*(x+4) + (1/4)*(4x-2) (distributing multiplication)
= (1/2)*(x) + (1/2)*(4) + (1/4)*(4x) + (1/4)*(-2) (distributing multiplication further)
= (1/2)*x + (1/2)*4 + (1/4)*4x + (1/4)*(-2) (simplifying multiplication)
= 1/2*x + 2 + (1/4)*4x + (1/4)*(-2) (simplifying addition)
= 1/2*x + 2 + 1*x + (-1/2) (simplifying multiplication and addition further)
= 1/2*x + x + 2 - 1/2 (simplifying the last two constants)
= (1/2 + 1)*x + (2 - 1/2) (combining like terms)
= (3/2)*x + (3/2) (simplifying further)

So, the simplified expression is (3/2)*x + 3/2.