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Simplify the expression. Write your answers using integers or improper fractions. 2k-(1)/(2)((1)/(2)k+2) Answer:

Simplify the expression. Write your answers using integers or improper fractions.\newline2k−12(12k+2) 2 k-\frac{1}{2}\left(\frac{1}{2} k+2\right) \newlineAnswer:

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Full solution

Q. Simplify the expression. Write your answers using integers or improper fractions.\newline2k−12(12k+2) 2 k-\frac{1}{2}\left(\frac{1}{2} k+2\right) \newlineAnswer:
  1. Distribute (1/2)(1/2): Distribute the (1/2)(1/2) across the terms inside the parentheses.\newline(1/2)((1/2)k+2)=(1/2)⋅(1/2)k+(1/2)⋅2(1/2)((1/2)k + 2) = (1/2)\cdot(1/2)k + (1/2)\cdot2
  2. Simplify multiplication: Simplify the multiplication inside the parentheses.\newline(12)∗(12)k=(14)k(\frac{1}{2})*(\frac{1}{2})k = (\frac{1}{4})k\newline(12)∗2=1(\frac{1}{2})*2 = 1\newlineSo, (12)((12)k+2)(\frac{1}{2})((\frac{1}{2})k + 2) becomes (14)k+1(\frac{1}{4})k + 1
  3. Rewrite with simplification: Rewrite the original expression with the simplified version of the parentheses. \newline2k−(12)(12k+2)2k - \left(\frac{1}{2}\right)\left(\frac{1}{2}k + 2\right) becomes 2k−(14k+1)2k - \left(\frac{1}{4}k + 1\right)
  4. Distribute negative sign: Distribute the negative sign across the terms in the parentheses. \newline2k−((1/4)k+1)=2k−(1/4)k−12k - ((1/4)k + 1) = 2k - (1/4)k - 1
  5. Combine like terms: Combine like terms.\newline2k−14k=84k−14k=74k2k - \frac{1}{4}k = \frac{8}{4}k - \frac{1}{4}k = \frac{7}{4}k\newlineSo, 2k−14k−12k - \frac{1}{4}k - 1 becomes 74k−1\frac{7}{4}k - 1
  6. Final simplified expression: The expression is now simplified. The final simplified expression is (74)k−1(\frac{7}{4})k - 1

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