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If x+x+1=2x+1, find the pos...

If x+x+1=2x+1, find the possible values of x.

A.

1 and -1

B.

-1 and 2

C.

1 and 2

D.

0 and -1

Correct answer is D

x+x+1=2x+1

Squaring both sides, we have

(x+x+1)2=(2x+1)2

x+2x(x+1)+x+1=2x+1

2x+1+2x(x+1)(2x+1)=0

(2x(x+1))2=024(x(x+1))=0

x = \text{0 or -1}