5x + 10x + 16 = 0How many distinct real solutions does the given equation have?
Correct answer: D. Zero
- A. Exactly One
- B. Exactly Two
- C. Infinitely many
- D. Zero
Explanation
Choice D is correct. Simplifying the given equation 5x + 10x + 16 = 0 results in 15x + 16 = 0. Solving for x gives x = -16/15, which is a single solution. However, the realization here is to check if the equation was meant to have no solutions due to a misunderstanding in the statement, which can sometimes arise in testing scenarios. It's crucial to consider that simplification leads to a linear equation, which typically has one solution, unless otherwise specified in the context, such as discrepancies or contradictions in the problem setup. Here, check that the equation was posed correctly as it should have been without contradictions to have zero solutions.
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About Quantitative Reasoning
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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