Question

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

Answer 1

To simplify the expression, we need to multiply each term by its respective fraction multipliers.

1/2 * (x + 4) becomes: 1/2 * x + 1/2 * 4, which simplifies to x/2 + 2.

1/4 * (4x - 2) becomes: 1/4 * 4x - 1/4 * 2, which simplifies to x - 1/2.

Now, we can add the simplified terms together: x/2 + 2 + x - 1/2.

To combine like terms, we first need to find a common denominator for x/2 and -1/2. The least common denominator is 2.

Multiplying the numerator and denominator of x/2 by 2 gives us 2x/4.

Therefore, the expression becomes: 2x/4 + 2 + x - 1/2.

Now, we can combine like terms: 2x/4 + x - 1/2 + 2.

To combine the mixed numbers with the fractions, we need to find a common denominator for 2x/4 and 1/2. The least common denominator is 4.

Multiplying the numerator and denominator of 2x/4 by 2 gives us 4x/8.

Therefore, the expression becomes: 4x/8 + x - 1/2 + 2.

Combining the terms gives us: (4x + 8x)/8 - 1/2 + 2.

Simplifying further, we get: 12x/8 - 1/2 + 2.

Now, we can convert the fraction 12x/8 into a mixed number. The fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 4.

So, the fraction becomes: 12x/8 = 3x/2.

Substituting this back into the expression, we get: 3x/2 - 1/2 + 2.

Combining the terms gives us: 3x/2 + 2 - 1/2.

To add the fraction and mixed number, we need to find a common denominator, which is 2.

Multiplying the numerator and denominator of 3x/2 by 2 gives us 6x/4.

Therefore, the expression becomes: 6x/4 + 2/1 - 1/2.

Combining the terms gives us: (6x + 8 - 2)/4 = (6x + 6)/4.

Therefore, the answer is (6x + 6)/4 in mixed number form.