Modded SAT Question Bank
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Test
Math
Domain
Algebra
Skill
Linear equations in one variable
Difficulty
Medium
ID: 12ee1edc
Modded SAT Question Bank by Abdullah Mallik

open parenthesis, b minus 2, close parenthesis, times x, equals 8

In the given equation, b is a constant. If the equation has no solution, what is the value of b ?

  1. 2

  2. 4

  3. 6

  4. 10

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Correct Answer: A
Rationale

Choice A is correct. This equation has no solution when there is no value of x that produces a true statement. Solving the given equation for x by dividing both sides by open parenthesis, b minus 2, close parenthesis gives x equals, the fraction with numerator 8, and denominator, open parenthesis, b minus 2, close parenthesis. When open parenthesis, b minus 2, close parenthesis, equals 0, the right-hand side of this equation will be undefined, and the equation will have no solution. Therefore, when b equals 2, there is no value of x that satisfies the given equation.

Choices B, C, and D are incorrect. Substituting 4, 6, and 10 for b in the given equation yields exactly one solution, rather than no solution, for x. For example, substituting 4 for b in the given equation yields open parenthesis, 4 minus 2, close parenthesis, times x, equals 8, or 2 x equals 8. Dividing both sides of 2 x equals 8 by 2 yields x equals 4. Similarly, if b equals 6 or b equals 10, x equals 2 and x equals 1, respectively.

Question Difficulty: Medium
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