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|x-1|=2

|x-1|=2 equation

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Numerical solution:

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The solution

You have entered [src] 
|x - 1| = 2
∣x−1∣=2\left|{x - 1}\right| = 2
Simplify
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
x−1≥0x - 1 \geq 0
or
1≤x∧x<∞1 \leq x \wedge x < \infty
we get the equation
(x−1)−2=0\left(x - 1\right) - 2 = 0
after simplifying we get
x−3=0x - 3 = 0
the solution in this interval:
x1=3x_{1} = 3

2.
x−1<0x - 1 < 0
or
−∞<x∧x<1-\infty < x \wedge x < 1
we get the equation
(1−x)−2=0\left(1 - x\right) - 2 = 0
after simplifying we get
−x−1=0- x - 1 = 0
the solution in this interval:
x2=−1x_{2} = -1


The final answer:
x1=3x_{1} = 3
x2=−1x_{2} = -1
The graph
05-15-10-51015020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -1
x1=−1x_{1} = -1 
x2 = 3
x2=3x_{2} = 3 
x2 = 3
Sum and product of roots [src] 
sum
-1 + 3
−1+3-1 + 3 
=
2
22 
product
-3
−3- 3 
=
-3
−3-3 
-3
Numerical answer [src] 
x1 = 3.0
x2 = -1.0
x2 = -1.0
The graph
|x-1|=2 equation
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