Full solution

Q. Simplify the expression. Write your answers using integers or improper fractions.

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2 k-\frac{1}{2}\left(\frac{1}{2} k+2\right)

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Answer:

Distribute $(1/2)$ : Distribute the $(1/2)$ across the terms inside the parentheses. $\newline$ $(1/2)((1/2)k + 2) = (1/2)\cdot(1/2)k + (1/2)\cdot2$
Simplify multiplication: Simplify the multiplication inside the parentheses. $\newline$ $(\frac{1}{2})*(\frac{1}{2})k = (\frac{1}{4})k$ $\newline$ $(\frac{1}{2})*2 = 1$ $\newline$ So, $(\frac{1}{2})((\frac{1}{2})k + 2)$ becomes $(\frac{1}{4})k + 1$
Rewrite with simplification: Rewrite the original expression with the simplified version of the parentheses. $\newline$ $2k - \left(\frac{1}{2}\right)\left(\frac{1}{2}k + 2\right)$ becomes $2k - \left(\frac{1}{4}k + 1\right)$
Distribute negative sign: Distribute the negative sign across the terms in the parentheses. $\newline$ $2k - ((1/4)k + 1) = 2k - (1/4)k - 1$
Combine like terms: Combine like terms. $\newline$ $2k - \frac{1}{4}k = \frac{8}{4}k - \frac{1}{4}k = \frac{7}{4}k$ $\newline$ So, $2k - \frac{1}{4}k - 1$ becomes $\frac{7}{4}k - 1$
Final simplified expression: The expression is now simplified. The final simplified expression is $(\frac{7}{4})k - 1$