Add: 1/2 (x+4)+1/4 (4x−2). Answer should be in mixed number form.
To simplify the expression, we first need to find a common denominator for the fractions. The least common multiple (LCM) of 2 and 4 is 4.
We then rewrite the expression with the common denominator:
1/2 (x+4) + 1/4 (4x-2) = (2/4)(x+4) + (1/4)(4x-2)
Now we can proceed to simplify:
= (2/4)x + (2/4)(4) + (1/4)(4x) - (1/4)(2)
= (2/4)x + 8/4 + 4/4 x - 2/4
= (2x/4) + (4x/4) + (8/4) - (2/4)
Now we can add the like terms:
= (2x + 4x + 8 - 2)/4
= (6x + 6)/4
To write the answer in mixed number form, we divide the numerator (6x + 6) by the denominator (4):
6x + 6 divided by 4 is 1 remainder 2.
Therefore, the expression simplifies to 1 and 2/4 or 1 and 1/2 in mixed number form.