Question

Subtract 1/2(z + 4) - 3(1/4z + 1).

Answer 1

To subtract the given expression, we need to simplify first:

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

First, let's simplify the fractions:

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

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

Now, let's distribute the -3 across the terms inside the parentheses:
-3(1/4z + 1) = -3 * (1/4)z - 3 * 1 = (3/4)z - 3

Now, we can substitute the simplified expressions back into the original expression and simplify further:

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

To add or subtract fractions, we need a common denominator. The least common denominator (LCD) of 2 and 4 is 4, so we need to multiply the first term by (2/2) and the second term by (4/4):

[(2/2)*(z + 4)]/2 - [(4/4)*(3/4)z] - 3

Simplifying:

(2z + 8)/2 - (12z/16) - 3

Now, let's combine the terms by finding a common denominator:

(2z + 8)/2 - (12z/16) - 3 = (8z + 32)/16 - (12z)/16 - 3

Now, we can subtract the terms:

(8z - 12z + 32)/16 - 3 = (-4z + 32)/16 - 3

To subtract fractions, we need a common denominator. The least common denominator (LCD) of 16 and 1 is 16, so we need to multiply the second term by (16/16):

(-4z + 32)/16 - 3*(16/16) = (-4z + 32)/16 - 48/16

Now, we can combine the terms:

(-4z + 32 - 48)/16 = (-4z - 16)/16

Finally, we can simplify further by factoring out a common factor of -4 from both terms:

-4(z + 4)/16 = -4/16 * (z + 4) = -1/4 * (z + 4)