Solve |x-2|=1/2x 1

Question

Solve the equation

x_{1} = \frac{4}{3}, x_{2} = 4

Alternative Form

x_{1} = 1. \dot{3}, x_{2} = 4

Evaluate

∣ x - 2 ∣ = \frac{1}{2} x \times 1

Multiply the terms

∣ x - 2 ∣ = \frac{1}{2} x

Rewrite the expression

∣ x - 2 ∣ - \frac{1}{2} x = 0

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

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

Solve the inequality

More Steps

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

Solve the equation

More Steps

x = 4, x \geq 2 x = \frac{4}{3}, x - 2 < 0

Solve the inequality

More Steps

x = 4, x \geq 2 x = \frac{4}{3}, x < 2

Find the intersection

x = 4 x = \frac{4}{3}, x < 2

Find the intersection

x = 4 x = \frac{4}{3}

Solution

x_{1} = \frac{4}{3}, x_{2} = 4

Alternative Form

x_{1} = 1. \dot{3}, x_{2} = 4

Show Solution