Let's solve each of these expressions step by step.
4)
\[ -2(8k + 8) - 3(5k - 1) \]
Distributing the terms: \[ = -2 \cdot 8k - 2 \cdot 8 - 3 \cdot 5k + 3 \cdot 1 \] \[ = -16k - 16 - 15k + 3 \] Combining like terms: \[ = -16k - 15k - 16 + 3 \] \[ = -31k - 13 \]
5)
\[ -8(2 - 2y) + 4(3 - 4y) \]
Distributing the terms: \[ = -8 \cdot 2 + 8 \cdot 2y + 4 \cdot 3 - 4 \cdot 4y \] \[ = -16 + 16y + 12 - 16y \] Combining like terms: \[ = -16 + 12 \] \[ = -4 \]
6)
\[ (3x - 11) / 2 - 5 - (4 - 3x) \]
First, rewrite the subtraction: \[ = (3x - 11) / 2 - 5 - 4 + 3x \]
Combine the constants: \[ = (3x - 11) / 2 + 3x - 9 \]
Now, to combine the terms, rewrite \( 3x \) over \( 2 \): \[ = (3x - 11)/2 + (6x - 18)/2 \] Combine: \[ = (3x + 6x - 11 - 18)/2 \] \[ = (9x - 29) / 2 \]
7)
\[ (Sa - 1) / (-6) + (3a - 7)(-2) \]
First rewrite the multiplication: \[ = (Sa - 1) / (-6) - 2(3a - 7) \] Expanding gives: \[ = (Sa - 1) / (-6) - 6a + 14 \]
This is simplified to: \[ = \frac{-(Sa - 1) + 6a(-6)}{6} + 14 \]
8)
\[ -0.5(-2x + 4) - (10 - x) \]
Distributing the first term: \[ = 1x - 2 - 10 + x \] \[ = x - 2 - 10 + x \] Combining like terms: \[ = 2x - 12 \]
Final Answers
\(-31k - 13\)
\(-4\)
\(\frac{9x - 29}{2}\)
(Answer requires more clarity on \(Sa\))
\(2x - 12\)
