Question

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

Answer should be in mixed number form. (1 point

Answer 1

To simplify the expression, we first distribute the coefficients to the terms inside the parentheses:

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

Next, simplify each term:

1/2*x = x/2
2/4*x = 2x/4 = x/2
1/4*-2 = -2/4 = -1/2

Now, we can rewrite the expression with the simplified terms:

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

To add the fractions with the same denominators, we add the numerators and keep the common denominator:

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

Since the fraction's numerator is greater than the denominator, we have a mixed number. We can rewrite it as follows:

2x + 3 divided by 2 = (2x + 3) ÷ 2 = 2x ÷ 2 + 3 ÷ 2 = x + 1 1/2

Therefore, the answer in mixed number form is x + 1 1/2.