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

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Bunuel
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If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   22 May 2020, 06:18
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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


PS21184
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E
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   22 May 2020, 06:22
Answer is supposedly E

Equation is x(x+1)=x+1
Let's put x=0
0(0+1)=0+1
0≠1 (incorrect)

Put x=1
1(1+1)=1+1
1(2)=2
2=2 (correct)

Put x=-1
-1(-1+1)=-1+1
-1(0)=0
0=0 (correct)

Only E is satisfying both 1&-1
Therefore Answer is E

Posted from my mobile device
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   22 May 2020, 06:25
Bunuel wrote:
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


PS21184


Test values... is more funny

-1
\(-1*(-1+1) = -1+1\)
\(-1(0) = 0\) Ok

0
\(0*(0+1)=0+1\)
\(0=1\) NO

1
\(1(1+1)=1+1\)
\(2=2\) OK

Answer E
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   22 May 2020, 06:39
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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 --> correct: x(x + 1) = x + 1 => x^2+x=x+1 =>x^2=1 => x=+1 or -1
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   22 May 2020, 07:14
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Bunuel wrote:
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


PS21184


RULE: Don't cancel the variable part (x+1 in this case)unless we know that it's non-zero


x(x + 1) - (x + 1) = (x+1)*(x-1) = 0

i.e. either x+1 = 0 or x-1 = 0

i.e. either x = -1 or x = 1

ANswer: Option E
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   22 May 2020, 08:09
Bunuel wrote:
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


PS21184

\(x(x + 1) = x + 1\)

Or, \(x^2 + x = x + 1\)

Or, \(x^2 = 1\)

Hence, \(x = -1\) & \(x = +1\), Answer must be (E)
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   24 May 2020, 09:22
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Bunuel wrote:
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
PS21184



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
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   25 May 2020, 10:55
x(x + 1) = x + 1

Do not cancel the (x+1) from both sides, its a trap.

Subtract (x+1) from both sides

x(x+1) - (x+1) = (x+1) - (x+1)
(x-1)(x+1) = 0

==> x = +1, -1

E.
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   31 May 2020, 04:12
Expert Reply
Bunuel wrote:
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



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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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   06 Jul 2020, 13:19
\(x(x + 1) = x + 1\)
\(x(x + 1) - (x + 1) = 0\)
\((x+1)(x-1)=0\)
\(x=-1\) or \(x=1\)

Answer E
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   09 Jul 2020, 11:06
Bunuel wrote:
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


PS21184


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

x(x + 1) = x + 1
(x+1)(x-1) = 0

x = 1 or -1

IMO E
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink] New post   10 Jun 2023, 07:51
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Re: If x(x + 1) = x + 1, what are all the possible values of x ? [#permalink]
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