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Algebra / Linear equations in one variable Difficulty: Medium

14x+5-13x+5=-7

What value of x  is the solution to the given equation?

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Explanation

Choice C is correct. For the given equation, x+5 is a factor of both terms on the left-hand side. Therefore, the given equation can be rewritten as 14-13x+5=-7, or 312-412x+5=-7, which is equivalent to -112x+5=-7. Multiplying both sides of this equation by -12 yields x+5=84. Subtracting 5 from both sides of this equation yields x=79

Choice A is incorrect. This is the value of x for which the left-hand side of the given equation equals 7 12 , not -7 .

Choice B is incorrect. This is the value of x for which the left-hand side of the given equation equals 0 , not -7 .

Choice D is incorrect. This is the value of x for which the left-hand side of the given equation equals - 209 12 , not -7 .