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Subtract 1/2(z+4)−3(1/4z+1)

. Use fractions in final form

1 answer

To simplify the expression \( -\frac{1}{2}(z + 4) - 3\left(\frac{1}{4}z + 1\right) \), we proceed as follows:

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

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

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

  4. Combine like terms. First, combine the \( z \) terms:

    • To do this, we find a common denominator. The least common denominator between 2 and 4 is 4. We can express \( -\frac{1}{2}z \) as \( -\frac{2}{4}z \): \[ -\frac{2}{4}z - \frac{3}{4}z = -\frac{5}{4}z \]

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

  6. Putting it all together, we have: \[ -\frac{5}{4}z - 5 \]

Thus, the final result of simplifying the expression \( -\frac{1}{2}(z + 4) - 3\left(\frac{1}{4}z + 1\right) \) is: \[ -\frac{5}{4}z - 5 \]