Let's simplify the expression step-by-step:
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Start with the expression:
\(-\frac{1}{2} ( z + 4 ) - 3 ( 1.4z + 1 )\). -
Distribute the \(-\frac{1}{2}\) and \(-3\) throughout their respective terms:
\(-\frac{1}{2}z - \frac{1}{2} \cdot 4 - 3 \cdot 1.4z - 3 \cdot 1\). -
This results in:
\(-\frac{1}{2}z - 2 - 4.2z - 3\). -
Combine the terms:
\(-\frac{1}{2}z - 4.2z - 2 - 3\). -
Combine the constants \(-2\) and \(-3\):
\(-\frac{1}{2}z - 4.2z - 5\). -
Now, to combine \(-\frac{1}{2}z\) and \(-4.2z\):
Convert \(-4.2z\) to a fraction: \(-4.2z = -\frac{42}{10}z = -\frac{21}{5}z\).Now convert \(-\frac{1}{2}z\) into a compatible fraction: \(-\frac{1}{2}z = -\frac{5}{10}z\).
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Now we can combine the terms: \(-\frac{5}{10}z - \frac{42}{10}z = -\frac{5 + 42}{10}z = -\frac{47}{10}z\).
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Therefore, the combined result is: \(-\frac{47}{10}z - 5\).
The final expression is: \[ -\frac{47}{10}z - 5. \]