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

Answer 1

To simplify 1/2(x+4)+1/4(4x-2), we start by distributing the fractions:

1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2

This simplifies to:

x/2 + 2/2 + 4x/4 - 2/4

The fraction 2/2 is equal to 1, and 4x/4 simplifies to x:

x/2 + 1 + x - 1/2

Combining like terms, we have:

x/2 + x + 1 - 1/2

To add the fractions together, we need to find a common denominator, which in this case is 2:

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

Combining the terms, we have:

(3x + 1)/2

Since the numerator is greater than the denominator, we can rewrite this as a mixed number:

1 1/2x