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Algebra / Linear equations in one variable Difficulty: Easy

If one half x, minus one sixth x, equals 1, what is the value of x ?

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Explanation

Choice C is correct. To make it easier to add like terms on the left-hand side of the given equation, both sides of the equation can be multiplied by 6, which is the lowest common denominator of one half and one sixth. This yields 3 x minus x, equals 6, which can be rewritten as 2 x equals 6. Dividing both sides of this equation by 2 yields x equals 3.

Choice A is incorrect and may result from subtracting the denominators instead of numerators with common denominators to get negative one fourth x, rather than one third x, on the left-hand side of the equation. Choice B is incorrect and may result from rewriting the given equation as one half x, equals one sixth instead of 2 x equals 6. Choice D is incorrect and may result from conceptual or computational errors.