Subtract 1/2(z+4)−3(1/4z+1)

Question

Use fractions in final form.(1 point)

Answer 1

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

1. Distribute \(-\frac{1}{2}\) to \((z + 4)\): \[ -\frac{1}{2}(z + 4) = -\frac{1}{2}z - 2 \]

2. Distribute \(-3\) to \(\left(\frac{1}{4}z + 1\right)\): \[ -3\left(\frac{1}{4}z + 1\right) = -\frac{3}{4}z - 3 \]

Now, we can combine the results: \[ -\frac{1}{2}z - 2 - \frac{3}{4}z - 3 \]

Next, combine the like terms. To do this, we need a common denominator for the \(z\) terms:

• The common denominator for \(-\frac{1}{2}\) and \(-\frac{3}{4}\) is \(4\).

Rewrite \(-\frac{1}{2}z\) in terms of fourths: \[ -\frac{1}{2}z = -\frac{2}{4}z. \]

Now combine the terms: \[ -\frac{2}{4}z - \frac{3}{4}z = -\frac{5}{4}z. \]

Now combine the constant terms: \[ -2 - 3 = -5. \]

Putting it all together, we arrive at the simplified expression: \[ -\frac{5}{4}z - 5. \]

Thus, the final answer is: \[ -\frac{5}{4}z - 5. \]