Subtract 1/2(z+4)−3(1/4z+1) . Use fractions in final form.
To subtract these fractions, we need to find a common denominator. The common denominator for 2 and 4 is 4.
Rewriting the fractions with the common denominator, we have:
1/2(z+4) becomes 2/4(z+4) = 2(z+4)/4
3(1/4z+1) becomes 3(1/4z+1) = 3(4z+4)/4
Now, subtracting the fractions:
2(z+4)/4 - 3(4z+4)/4
To combine the fractions, we can multiply the numerators by the denominators of the other fraction:
(2(z+4) - 3(4z+4))/4
Expanding:
(2z+8 - 12z-12)/4
Simplifying:
(-10z - 4)/4
Final form:
-10z/4 - 4/4
Reducing the fraction:
-5z/2 - 1