What are all the solutions for x if 3x2 - 2x-21= 0?
Correct answer: E. x= 3 or x = -7/3
- A. x = -21 only
- B. x = -7 or x = 3
- C. x = -3 or x = 7/3
- D. x = -7/3 or x = -3
- E. x= 3 or x = -7/3
Explanation
Split the middle term into two terms: 3x²-9x+7x-21=0 Factor the first two terms and the last two terms separately: 3x(x-3)+7(x-3)=0 Factor out: (x-3) (3x+7)=0 Apply Zero Product Property: 2-3=0 or 3x+7=0 Rearrange unknown terms to the left side of the equation: 2 =3 Rearrange unknown terms to the left side of the equation: 3x =-7 Divide both sides of the equation by the coefficient of variable: =-7÷3 Rewrite as fraction: -3/7 Combine the results: x =3 or x=-7/3 Answer: x=3 or =- 7 /3
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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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