Solve for X /x+1/ + /x-1/ = 1 HOW !?

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Answer 1

Anything bounded by "|" is the "absolute value".

Solve for x, where:
| x + 1 | + | x - 1 | = 1

Absolute value of the first term is x + 1.
Absolute value of the second term is x - 1.

Simplify:
x + 1 + x -1 = 1
2x + 0 = 1
x = ½
...........................
Check your answer:
| ½ + 1 | + | ½ - 1 | = 1

Absolute value of the first term is 1½.
Absolute value of the second term is ½.

1½ + ½ ≠ 1

►►WHOOPS!◄◄

THERE IS NO SOLUTION

Answer 2

Answer is definitely not x = 1/2.

If you plug in x = 1/2 into the equation, you get

2 = 1 which is false.



I suspect the answer is no solution. Why?

|x+1| + |x - 1| = 1

|x-1| = 1 - |x+1|

Let y = |x-1| and y = 1 - |x+1|

We want to plot the 2 graphs and find the intersection point(s) of the two graphs. If they don't intesect, there is no solution.

Plotting the 2 graphs, the 2 graphs indeed don't intersect at all.

Hence, there is no solution!

This is provided that I have interpreted /x+1/ as |x+1| (modulus sign).


P/S

This is what kae has shown:
x /x+1/ + /x-1/ = 1
x (x+1) + (x-1) = 1

I am afraid you cannot remove the modulus sign as you like.

ie. |x+1| is not equals to (x+1)

Answer 3

the solution for this equation /x+1/ + /x-1/ = 1 is

taking the absolute value of both terms, the then becomes
x+1 + x-1 = 1
so the solution would be
2x = 1
therefore x = 1/2 or 0.5

however:
X /x+1/ + /x-1/ = 1, if the symbol / in /x+1/ denotes absolute value the the solution to the equation would be:

x /x+1/ + /x-1/ = 1
x (x+1) + (x-1) = 1
x^2 + x + x - 1 = 1
x^2 + 2x - 1 = 1
x^2 + 2x = 1 + 1
x^2 + 2x -2 = 0
by quadratic equation:

x = (-2+/- sq rt of (4- 4*-2)} / 2
x = {-2 +/- 2 *sq rt of 2} / 2
x = {-2 +/- 2 * 1.414} / 2
x = {-2 +/- 2.828} / 2

there would be 2 values for x
x = 0.414 and x = -2.414

Hope this helps...

Answer 4

When there is an addition sign in between the two in parentheses you can just take the parentheses off.

So,

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

is the same as

x + 1 + x - 1 = 1

Simplify this into:

2x + (1 - 1) = 1

2x + 0 = 1

2x = 1

x = 1/2

Hope this helps!

Answer 5

|x+1| + |x-1| = 1
It can be solved as follows.

If x>=1, x+1>0 & x-1>0
So, 2x=1 & x=1/2
But if we put x=1/2 in the equation,
3/2 + 1/2 is not equal to 1.
So, no solution in this interval.

If -1= x+1>=0 & x-1<=0
So, x+1 + -(x-1) =1
which gives 2=1 (i.e. contradictory)
So, no solution in this interval too.

If x<-1
x+1<0 & x-1<0
So, -(1+x) + -(1-x)=1
which gives -2=1 (i.e. contradictory)
So, no solution in this interval too.

Hence, equation has no solution.

Answer 6

x+1+x-1=1 2x=1
x=1/2

Answer 7

|x + 1| + |x - 1| = 1

No Solution

Like most, i got (1/2), but if you plug in (1/2) for x, you will get 2 and not 1 on the left side.

Answer 8

if x<-1 eq is absurd ,if -11, x=1/2 is the answer I THINK SO

Answer 9

Just what are the "/"s supposed to mean in your equation?
Are they meant to be division signs?
Are they meant to be the equivalent of parentheses?
Are they meant to represent absolute value?
Or do they mean something else entirely?

Until you clearify that, the equation cannot be solved because it is unclear what it (you) means.

PS: You should use standard mathematical notation when possible.