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# Help me solve an inequality question

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#### tomcenjerrym

##### Newbie level 4
Does anyone can solve the following equation?

|x − 1| = 1 − x

Thanks

Tom

Re: Inequality question

x=1 is the solution.... when x-1 is assumed to be negative we cannot obtain the solution....

Re: Inequality question

just do a variable change y=x-1 and -y=1-x, so we will get Abolute value of y=-y so the only number that fits this equation is y=0 so if x-1=0 the solution is x=1.

Re: Inequality question

The solution is : x= ] - ∞ 1]

This because any value of x less than or equlal to 1 would satisfy the equation

Re: Inequality question

All of you must remind a well-known definition of the absolute number's value. It states the following:

|a| = a, if a>=0
= -a, otherwise

Therefore, your example |x − 1| = 1 − x results in the inequality:

x - 1 <= 0
x <=1

It's one of these unique rare cases when inequality is the satisfactory solution of the equation (usually, it's a number or some ones)

With respect,

Dmitij

Re: Inequality question

x<=-1

Re: Inequality question

Use |x|=x if x>0 and |x|=-x if x<0

thus the eqn presents no soluton for |x-1|>0.... But all values are satisfying the soln. for |x-1|<0

Re: Inequality question

| x - 1 | = 1 - x = - ( x -1 )
this means that x -1 < 0 (((( not x - 1 <= 0 )))) >>> some of the replies are wrong

>> x - 1 < 0 >>> x < 1

solution : (-∞ , 1 ]

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