Question
Solve the equation
x1=21,x2=23
Alternative Form
x1=0.5,x2=1.5
Evaluate
∣x−∣x−2∣∣=1
Separate the equation into 2 possible cases
x−∣x−2∣=1x−∣x−2∣=−1
Solve the equation for x
More Steps

Evaluate
x−∣x−2∣=1
Move the expression to the left side
x−∣x−2∣−1=0
Separate the equation into 2 possible cases
x−(x−2)−1=0,x−2≥0x−(−(x−2))−1=0,x−2<0
The statement is false for any value of x
More Steps

Evaluate
x−(x−2)−1=0
Calculate
x−x+2−1=0
Calculate the sum or difference
1=0
The statement is false for any value of x
x∈∅
x∈∅,x−2≥0x−(−(x−2))−1=0,x−2<0
Solve the inequality
More Steps

Evaluate
x−2≥0
Move the constant to the right side
x≥0+2
Removing 0 doesn't change the value,so remove it from the expression
x≥2
x∈∅,x≥2x−(−(x−2))−1=0,x−2<0
Solve the equation
More Steps

Evaluate
x−(−(x−2))−1=0
Calculate
x+x−2−1=0
Calculate the sum or difference
2x−3=0
Move the constant to the right-hand side and change its sign
2x=0+3
Removing 0 doesn't change the value,so remove it from the expression
2x=3
Divide both sides
22x=23
Divide the numbers
x=23
x∈∅,x≥2x=23,x−2<0
Solve the inequality
More Steps

Evaluate
x−2<0
Move the constant to the right side
x<0+2
Removing 0 doesn't change the value,so remove it from the expression
x<2
x∈∅,x≥2x=23,x<2
Find the intersection
x∈∅x=23,x<2
Find the intersection
x∈∅x=23
Find the union
x=23
x=23x−∣x−2∣=−1
Solve the equation for x
More Steps

Evaluate
x−∣x−2∣=−1
Move the expression to the left side
x−∣x−2∣−(−1)=0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x−∣x−2∣+1=0
Separate the equation into 2 possible cases
x−(x−2)+1=0,x−2≥0x−(−(x−2))+1=0,x−2<0
The statement is false for any value of x
More Steps

Evaluate
x−(x−2)+1=0
Calculate
x−x+2+1=0
Calculate the sum or difference
3=0
The statement is false for any value of x
x∈∅
x∈∅,x−2≥0x−(−(x−2))+1=0,x−2<0
Solve the inequality
More Steps

Evaluate
x−2≥0
Move the constant to the right side
x≥0+2
Removing 0 doesn't change the value,so remove it from the expression
x≥2
x∈∅,x≥2x−(−(x−2))+1=0,x−2<0
Solve the equation
More Steps

Evaluate
x−(−(x−2))+1=0
Calculate
x+x−2+1=0
Calculate the sum or difference
2x−1=0
Move the constant to the right-hand side and change its sign
2x=0+1
Removing 0 doesn't change the value,so remove it from the expression
2x=1
Divide both sides
22x=21
Divide the numbers
x=21
x∈∅,x≥2x=21,x−2<0
Solve the inequality
More Steps

Evaluate
x−2<0
Move the constant to the right side
x<0+2
Removing 0 doesn't change the value,so remove it from the expression
x<2
x∈∅,x≥2x=21,x<2
Find the intersection
x∈∅x=21,x<2
Find the intersection
x∈∅x=21
Find the union
x=21
x=23x=21
Solution
x1=21,x2=23
Alternative Form
x1=0.5,x2=1.5
Show Solution
