Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form

Answer 1

To solve the expression 1/2(x+4) + 1/4(4x-2), we first distribute the fractions:

1/2(x+4) + 1/4(4x-2) = 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2

Simplifying further:

= (1/2)x + (1/2)*4 + (1/4)*4x - (1/4)*2
= (1/2)x + 2 + x - 1/2
= (1/2)x + x + 2 - 1/2
= (1/2 + 2/2)x + 4/2 - 1/2
= (3/2)x + 4/2 - 1/2
= (3/2)x + 3/2
= (3x + 3)/2

Therefore, the answer in mixed number form is (3x + 3)/2.