Subtract 1/2 (z+4) –3 (1/4z+1). Use fractions in final form.
To subtract these fractions, we need a common denominator. The least common multiple of 2 and 4 is 4, so we can rewrite the expression with a denominator of 4:
1/2 (z+4) – 3 (1/4z+1) = (1/2)(2/2)(z+4) - 3(1/4)(4/4)(z+1)
Simplifying the fractions:
= (1/2)(2z + 8) - 3(1/4)(z + 1)
= (z + 8) - 3/4(z + 1)
= z + 8 - (3/4)(z + 1)
= z + 8 - (3/4)z - 3/4
Combining like terms:
= z - (3/4)z + 8 - 3/4
= (1 - 3/4)z + (8 - 3/4)
= (1/4)z + (32/4 - 3/4)
= (1/4)z + (29/4)
Therefore, the final form of the expression is (1/4)z + (29/4).