lionsshare wrote:If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

OA: E

Please explain the solution to this problem. Thank you.

1 + 1/x = 2 - 2/x

Transposing 2/x to left-hand side and 1 to the right-hand side, we get

1/x + 2/x = 2 - 1

3/x = 1

Cross-multiplying, we get 3 = 1*x => x = 3.

The correct answer: E

Hope this helps!

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lionsshare wrote:If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

OA: E

Another approach is to eliminate the fractions at step 1.
Given: 1 + 1/x = 2 - 2/x
Multiply both sides by x to get: x + 1 = 2x - 2
Add 2 to both sides: x + 3 = 2x
Subtract x from both sides: 3 = x

Answer: E

Hi lionsshare,

Based on the 'design' of this question and the answer choices, you can use the answers 'against' the prompt and TEST THE ANSWERS.

We're told that 1 + 1/X = 2 - 2/X

In simple terms, we're adding something to "1" and subtracting something else from "2" and ending with the same result. This means that each 'side' of the equation is the same value - and that value is something BETWEEN 1 and 2. Thus, whatever we're adding to 1 and subtracting from 2 must be POSITIVE FRACTIONS. Only two of the answer choices, when placed as the value of X, will create positive fractions: Answers D and E.

IF... X = 2, then the two sides of the equation are...
1 + 1/2 = 1.5
2 - 2/2 = 1
These results are NOT equal, so D is NOT the answer.

IF... X = 3, then the two sides of the equation are...
1 + 1/3 = 4/3
2 - 2/3 = 6/3 - 2/3 = 4/3
These results ARE equal, so E is the answer.

Final Answer: E

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