Solve |x-1| ^|x-3| = 1

Question

Solve the equation

x = \frac{1 + 17}{2}

Alternative Form

x \approx 2.561553

Evaluate

∣ x - 1 ∣ \times x - 3 = 1

Calculate

x ∣ x - 1 ∣ - 3 = 1

Move the expression to the left side

x ∣ x - 1 ∣ - 3 - 1 = 0

Subtract the numbers

x ∣ x - 1 ∣ - 4 = 0

Separate the equation into 2 possible cases

x (x - 1) - 4 = 0, x - 1 \geq 0 x (- (x - 1)) - 4 = 0, x - 1 < 0

Solve the equation

More Steps

x = \frac{1 + 17}{2} x = \frac{1 - 17}{2}, x - 1 \geq 0 x (- (x - 1)) - 4 = 0, x - 1 < 0

Solve the inequality

More Steps

x = \frac{1 + 17}{2} x = \frac{1 - 17}{2}, x \geq 1 x (- (x - 1)) - 4 = 0, x - 1 < 0

Solve the equation

More Steps

x = \frac{1 + 17}{2} x = \frac{1 - 17}{2}, x \geq 1 x \in / R, x - 1 < 0

Solve the inequality

More Steps

x = \frac{1 + 17}{2} x = \frac{1 - 17}{2}, x \geq 1 x \in / R, x < 1

Find the intersection

x = \frac{1 + 17}{2} x \in / R, x < 1

Find the intersection

x = \frac{1 + 17}{2} x \in / R

Solution

x = \frac{1 + 17}{2}

Alternative Form

x \approx 2.561553

Show Solution