If x(x + 1) = x + 1, what are all the possible values of x ?
A. -1 only
B. 0 only
C. 1 only
D. -1 and 0
E. -1 and 1
Answer: E
Source: GMAT prep
If x(x + 1) = x + 1, what are all the possible values of x ?
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Given: x(x + 1) = x + 1BTGModeratorVI wrote: ↑Mon May 25, 2020 7:33 amIf x(x + 1) = x + 1, what are all the possible values of x ?
A. -1 only
B. 0 only
C. 1 only
D. -1 and 0
E. -1 and 1
Answer: E
Source: GMAT prep
Note: Some students will be tempted to divide both sides of the equation by (x + 1) to get x = 1.
However, since we don't know the value of x, we may be inadvertently dividing both sides by 0, which is a big no-no
Instead, let's first expand the left side to get: x² + x = x + 1
Subtract x from both sides: x² = 1
From here we can see that, EITHER x = 1 OR x = -1
Answer: E
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Solution:BTGModeratorVI wrote: ↑Mon May 25, 2020 7:33 amIf x(x + 1) = x + 1, what are all the possible values of x ?
A. -1 only
B. 0 only
C. 1 only
D. -1 and 0
E. -1 and 1
Answer: E
Source: GMAT prep
If x = -1, we see that both sides of the equation will be 0. Thus, a value of x is -1.
If x ≠ -1, divide both sides of the equation by x + 1 and we’ll have x = 1. Thus, another value of x is 1.
Answer: E
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