Solve |1 - x| = x - 1

Question

Solve the equation

x \geq 1

Alternative Form

x \in [1, + \infty)

Evaluate

∣ 1 - x ∣ = x - 1

Rewrite the expression

∣ 1 - x ∣ - x + 1 = 0

Separate the equation into 2 possible cases

1 - x - x + 1 = 0, 1 - x \geq 0 - (1 - x) - x + 1 = 0, 1 - x < 0

Solve the equation

More Steps

Evaluate

1 - x - x + 1 = 0

Calculate the sum or difference

More Steps

Evaluate

1 - x - x + 1

Add the numbers

2 - x - x

Subtract the terms

2 - 2 x

2 - 2 x = 0

Move the constant to the right-hand side and change its sign

- 2 x = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

- 2 x = - 2

Change the signs on both sides of the equation

2 x = 2

Divide both sides

\frac{2 x}{2} = \frac{2}{2}

Divide the numbers

x = \frac{2}{2}

Divide the numbers

More Steps

Evaluate

\frac{2}{2}

Reduce the numbers

\frac{1}{1}

Calculate

1

x = 1

x = 1, 1 - x \geq 0 - (1 - x) - x + 1 = 0, 1 - x < 0

Solve the inequality

More Steps

Evaluate

1 - x \geq 0

Move the constant to the right side

- x \geq 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- x \geq - 1

Change the signs on both sides of the inequality and flip the inequality sign

x \leq 1

x = 1, x \leq 1 - (1 - x) - x + 1 = 0, 1 - x < 0

The statement is true for any value of x

More Steps

Evaluate

- (1 - x) - x + 1 = 0

Calculate

- 1 + x - x + 1 = 0

Calculate the sum or difference

More Steps

Evaluate

- 1 + x - x + 1

Since two opposites add up to 0,remove them form the expression

x - x

Subtract the terms

0

0 = 0

The statement is true for any value of x

x \in R

x = 1, x \leq 1 x \in R, 1 - x < 0

Solve the inequality

More Steps

Evaluate

1 - x < 0

Move the constant to the right side

- x < 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- x < - 1

Change the signs on both sides of the inequality and flip the inequality sign

x > 1

x = 1, x \leq 1 x \in R, x > 1

Find the intersection

x = 1 x \in R, x > 1

Find the intersection

x = 1 x > 1

Solution

x \geq 1

Alternative Form

x \in [1, + \infty)

Show Solution

Solve the equation

Graph