Subtract 1/2(z+4)−3(1/4z+1). 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 start by distributing within both terms:

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

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

Now we put these results back into the expression: \[ \frac{1}{2}z + 2 - \left(\frac{3}{4}z + 3\right) \]

Next, distribute the negative sign: \[ \frac{1}{2}z + 2 - \frac{3}{4}z - 3 \]

Now, combine like terms:

1. Combine the \( z \) terms: \[ \frac{1}{2}z - \frac{3}{4}z \] To add these fractions, we can convert \( \frac{1}{2}z \) to have a common denominator of 4: \[ \frac{1}{2}z = \frac{2}{4}z \] Thus, \[ \frac{2}{4}z - \frac{3}{4}z = -\frac{1}{4}z \]

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

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

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