Solve \sqrt (2x-1)<x

Evaluate

2 x - 1 < x

Find the domain

More Steps

2 x - 1 < x, x \geq \frac{1}{2}

Separate the inequality into 2 possible cases

2 x - 1 < x, x \geq 0 2 x - 1 < x, x < 0

Solve the inequality

More Steps

x \neq = 1, x \geq 0 2 x - 1 < x, x < 0

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x

x \neq = 1, x \geq 0 x \in \emptyset, x < 0

Find the intersection

x \in [0, 1) \cup (1, + \infty) x \in \emptyset, x < 0

Find the intersection

x \in [0, 1) \cup (1, + \infty) x \in \emptyset

Find the union

x \in [0, 1) \cup (1, + \infty)

Check if the solution is in the defined range

x \in [0, 1) \cup (1, + \infty), x \geq \frac{1}{2}

Solution

x \in [\frac{1}{2}, 1) \cup (1, + \infty)