Solve |1/3x-2|=2x

Question

Solve the equation

x = \frac{6}{7}

Alternative Form

x = 0. \dot{8} 5714 \dot{2}

Evaluate

\frac{1}{3} x - 2 = 2 x

Rewrite the expression

\frac{1}{3} x - 2 - 2 x = 0

Separate the equation into 2 possible cases

\frac{1}{3} x - 2 - 2 x = 0, \frac{1}{3} x - 2 \geq 0 - (\frac{1}{3} x - 2) - 2 x = 0, \frac{1}{3} x - 2 < 0

Solve the equation

More Steps

x = - \frac{6}{5}, \frac{1}{3} x - 2 \geq 0 - (\frac{1}{3} x - 2) - 2 x = 0, \frac{1}{3} x - 2 < 0

Solve the inequality

More Steps

x = - \frac{6}{5}, x \geq 6 - (\frac{1}{3} x - 2) - 2 x = 0, \frac{1}{3} x - 2 < 0

Solve the equation

More Steps

x = - \frac{6}{5}, x \geq 6 x = \frac{6}{7}, \frac{1}{3} x - 2 < 0

Solve the inequality

More Steps

x = - \frac{6}{5}, x \geq 6 x = \frac{6}{7}, x < 6

Find the intersection

x \in \emptyset x = \frac{6}{7}, x < 6

Find the intersection

x \in \emptyset x = \frac{6}{7}

Solution

x = \frac{6}{7}

Alternative Form

x = 0. \dot{8} 5714 \dot{2}

Show Solution