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13(x - 2) + 1x - 2 - 12(x - 2) = -56. What is the value of x?

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by Max@Math Revolution » Fri Jul 10, 2020 1:01 am

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[GMAT math practice question]

1/3(x - 2) + 1/x - 2 - 1/2(x - 2) = -5/6. What is the value of x?

A. 1
B. 4
C. 7
D. 8
E. 9
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Re: 13(x - 2) + 1x - 2 - 12(x - 2) = -56. What is the value of x?

by Max@Math Revolution » Sun Jul 12, 2020 6:49 pm
=>

First, let’s simplify the left-hand side of the equation.
1/3(x - 2) + 1/x - 2 - 1/2(x - 2)
= 2/6(x - 2) + 6/6(x - 2) - 3/6(x - 2)
= 5/6(x - 2)

Now, let’s set our simplified equation equal to the original right-hand side.
5/6(x - 2) = -5/6

If we cancel out 56 from both sides, we have:
1/x - 2 = -1
⇔ 1 = -1(x – 2)
⇔ 1 = -x + 2
⇔ x = 2 – 1
⇔ x = 1

Therefore, A is the correct answer.
Answer: A
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