Question

Add: 1/2(x + 4) + 1/4(4x - 2). Express the answer in mixed number form.

Answer 1

To add 1/2(x + 4) + 1/4(4x - 2), distribute the fractions, combine like terms, and express the result in mixed number form. The final expression is (3/2)x + (3/2), which does not naturally simplify to a mixed number unless x is such that it allows for this conversion.

Step-by-step explanation:

The question requires adding two algebraic fractions and expressing the result in mixed number form. To solve this, we first need to distribute the fractions into the parentheses:

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

This simplifies to:

• 1/2*x + 2
• 1*x - 1/2

Now we combine like terms:

• (1/2 + 1)x + (2 - 1/2)

The sum is:

• (3/2)x + (3/2)

Expressed as a mixed number, the coefficient of x and the constant term remain as improper fractions or can be converted if they result in whole number values plus proper fractions. In our case, both coefficients are fractional and do not simplify to a mixed number unless x has a value that allows for such conversion.