Question

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

Answer 1

To simplify the expression, we need to multiply the fractions and combine like terms.

Start with the first fraction: 1/2(x + 4). To multiply 1/2 by (x + 4), distribute the 1/2 to each term in the parentheses, giving us:
1/2 * x = (1/2)x
1/2 * 4 = (1/2) * 4 = 2

So, 1/2(x + 4) simplifies to (1/2)x + 2.

Now, move on to the second fraction: 1/4(4x - 2). Again, distribute the 1/4 to each term in the parentheses:
1/4 * 4x = (1/4) * 4x = x
1/4 * -2 = (1/4)(-2) = -1/2

So, 1/4(4x - 2) simplifies to x - 1/2.

Now, we can combine the simplified fractions: (1/2)x + 2 + x - 1/2.

To combine the fractions, we need to have a common denominator. The denominators here are 2 and 1. To find a common denominator, we can multiply them together: 2 * 1 = 2.

Now, rewrite the fractions with the common denominator:
(1/2)x + 2 + 2(1/1)x - 1(1/2).

Simplify the second fraction: 2(1/1)x = 2x.

Combine the fractions: (1/2)x + 2 + 2x - 1/2.

Combine the constant terms: 2 + (-1/2) = 1 1/2. To express this as a mixed number, divide the numerator (1) by the denominator (2), which gives 1/2. The whole number part of the mixed number is 1. So, 1 1/2 as a mixed number is 1 1/2.

Thus, the simplified expression 1/2(x + 4) + 1/4(4x - 2) is (1/2)x + 2 + 2x - 1/2, which further simplifies to 3/2x + 3/2 or as a mixed number, 1 1/2x + 1 1/2.