If x(x + 1) = x + 1, what are all the possible values of x ?

BTGModeratorVI wrote: ↑

Thu Nov 26, 2020 1:11 pm

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

Given: x(x + 1) = x + 1
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

Cheers,
Brent

BTGModeratorVI wrote: ↑

Thu Nov 26, 2020 1:11 pm

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

Solution:

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