Question

Subtract 1/2(z+4)−3(1/4z+1). Use fractions in final form.

Answer 1

To subtract the given expression, we need to distribute the coefficients to their respective terms.

First, distribute the 1/2 to (z+4):

1/2 * (z+4) = (1/2)*(z) + (1/2)*(4) = 1/2z + 2

Next, distribute the -3 to (1/4z+1):

-3 * (1/4z+1) = (-3)*(1/4z) + (-3)*(1) = -3/4z - 3

Now we can subtract the two terms:

1/2z + 2 - 3/4z - 3

To simplify this expression, we need to find a common denominator for the fractions. The common denominator is 4, so we multiply the first term by 2/2 and the second term by 4/4:

(1/2)*(z/1)*(2/2z) + 2*(2/2) - (3/4z)*(4/4) - 3*(4/4)

This gives us:

(2z/4z) + 4/2 + (-12/4z) - 12/4

Simplifying each term:

(2z + 4) - (3z) - 3

Combining like terms:

2z - 3z + 4 - 3

Simplifying again:

-z + 1

So the final simplified form of the expression is -z + 1 in fraction form.