To simplify the expression \( 5(0.5k - 1) + 2(0.4 - k) \), we will distribute the coefficients into the parentheses.
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Distribute \( 5 \) into \( (0.5k - 1) \): \[ 5(0.5k) - 5(1) = 2.5k - 5 \]
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Distribute \( 2 \) into \( (0.4 - k) \): \[ 2(0.4) - 2(k) = 0.8 - 2k \]
Now, combine the results from both distributions: \[ 2.5k - 5 + 0.8 - 2k \]
Next, combine the like terms:
- For the \( k \) terms: \( 2.5k - 2k = 0.5k \)
- For the constant terms: \( -5 + 0.8 = -4.2 \)
Putting it all together, we have: \[ 0.5k - 4.2 \]
Thus, the simplified expression is: \[ \boxed{0.5k - 4.2} \]