Subtract 1/2(z+4)−3(1/4z+1)

Question

. Use fractions in final form.(1 point)

Answer 1

To subtract the expression \( \frac{1}{2}(z + 4) - 3\left(\frac{1}{4}z + 1\right) \), we will first distribute the terms.

1. Distributing \( \frac{1}{2}(z + 4) \): \[ \frac{1}{2}z + \frac{1}{2} \cdot 4 = \frac{1}{2}z + 2 \]

2. Distributing \( 3\left(\frac{1}{4}z + 1\right) \): \[ 3 \cdot \frac{1}{4}z + 3 \cdot 1 = \frac{3}{4}z + 3 \]

Now, we can rewrite the expression with the distributed terms: \[ \left(\frac{1}{2}z + 2\right) - \left(\frac{3}{4}z + 3\right) \]

Next, we need to subtract the second expression from the first: \[ \frac{1}{2}z + 2 - \frac{3}{4}z - 3 \]

Combining like terms, let's first focus on the \( z \) terms: \[ \frac{1}{2}z - \frac{3}{4}z = \frac{2}{4}z - \frac{3}{4}z = -\frac{1}{4}z \]

Now for the constant terms: \[ 2 - 3 = -1 \]

Putting it all together, we have: \[ -\frac{1}{4}z - 1 \]

So the final result is: \[ -\frac{1}{4}z - 1 \]