(1/2x+1) + 5Which of the following is equivalent to the expression above for x > 0?
Correct answer: D. 10x + 6/2x + 1
- A. (2x + 5)/(2x + 1)
- B. (2x + 6)/(2x + 1)
- C. (10x + 5)/(2x + 1)
- D. 10x + 6/2x + 1
Explanation
The correct answer is (10x + 6)/(2x + 1). To solve the expression (1/(2x+1)) + 5, you must first express the whole number 5 as a fraction with the same denominator: 5 * (2x+1)/(2x+1). This becomes (5(2x+1))/(2x+1) or (10x+5)/(2x+1). Adding this to (1/(2x+1)), the numerators combine to (10x+5+1), giving (10x+6)/(2x+1). The other options either incorrectly combine terms or misapply the process of finding a common denominator.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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