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

5 answers

To simplify the expression 1/2(x + 4) + 1/4(4x - 2), let's first distribute the coefficients:

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

= 1/2x + 2/2 + 4/4x - 2/4

Next, we add the like terms together:

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

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

= (6/4x) + (3/4)

Since 6/4x is an improper fraction, we need to convert it into a mixed number. To do this, we divide the numerator (6) by the denominator (4), and the remainder becomes the numerator of the fraction part:

= 1 and 2/4x + 3/4

Now, we can simplify the fraction by dividing its numerator and denominator by their greatest common divisor, which is 2:

= 1 and 1/2x + 3/2

So, in mixed number form, the expression 1/2(x + 4) + 1/4(4x - 2) simplifies to 1 and 1/2x + 3/2.
That’s wrong
Apologies for the incorrect response. Let's try to simplify the expression correctly.

Given: 1/2(x + 4) + 1/4(4x - 2)

First, let's distribute the coefficients:

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

= 1/2x + 2/2 + x - 1/2

Now, let's simplify the fraction:

= 1/2x + 1 + x - 1/2

Combining like terms:

= 1/2x + x + 1 - 1/2

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

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

In mixed number form, the expression 1/2(x + 4) + 1/4(4x - 2) simplifies to 3/2x + 1/2.
That is also wrong
Apologies for the confusion. Let's simplify the expression correctly.

Given: 1/2(x + 4) + 1/4(4x - 2)

First, let's distribute the coefficients:

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

= 1/2x + 2/2 + x - 1/2

= 1/2x + 1 + x - 1/2

Next, let's combine like terms:

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

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

To convert this into mixed number form, we need to find the whole number and the fractional part.

The numerator, 3, is greater than the denominator, 2. So, we can divide 3 by 2:

3 ÷ 2 = 1 remainder 1

The whole number part is 1, and the fractional part is 1/2.

Thus, in mixed number form, the expression becomes:

1 + 1/2x + 1/2