To simplify the expression \( \frac{6}{5}k + \frac{9}{5} - 2k + \frac{2}{5} + \frac{2}{5}k - 5 \), let's combine the like terms step-by-step.
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Combine the \( k \) terms: \[ \frac{6}{5}k - 2k + \frac{2}{5}k \] First, convert \( 2k \) to a fraction that has a denominator of 5: \[ -2k = -\frac{10}{5}k \] Now, combine: \[ \frac{6}{5}k - \frac{10}{5}k + \frac{2}{5}k = \left( \frac{6 - 10 + 2}{5} \right)k = \frac{-2}{5}k \]
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Combine the constant terms: \[ \frac{9}{5} + \frac{2}{5} - 5 \] First, combine \( \frac{9}{5} \) and \( \frac{2}{5} \): \[ \frac{9 + 2}{5} = \frac{11}{5} \] Now convert \( -5 \) to a fraction: \[ -5 = -\frac{25}{5} \] Finally, combine these: \[ \frac{11}{5} - \frac{25}{5} = \frac{11 - 25}{5} = \frac{-14}{5} \]
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Put it all together: The simplified expression is: \[ \frac{-2}{5}k + \frac{-14}{5} \]
So, the final answer is: \[ \frac{-2}{5}k - \frac{14}{5} \]
You can also write it as: \[ -\frac{2}{5}k - \frac{14}{5} \]
Either format is acceptable.