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

Question

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

Accepted Answer

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 gives . When , the right-hand side of this equation will be undefined, and the equation will have no solution. Therefore, when , 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 , or . Dividing both sides of by 2 yields . Similarly, if or , and , respectively.

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