Solve x(2x-1) < 2x

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

0 < x < \frac{3}{2}

Alternative Form

x \in (0, \frac{3}{2})

Evaluate

x (2 x - 1) < 2 x

Move the expression to the left side

x (2 x - 1) - 2 x < 0

Subtract the terms

More Steps

2 x^{2} - 3 x < 0

Rewrite the expression

2 x^{2} - 3 x = 0

Factor the expression

More Steps

x (2 x - 3) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 2 x - 3 = 0

Solve the equation for x

More Steps

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

Determine the test intervals using the critical values

x < 0 0 < x < \frac{3}{2} x > \frac{3}{2}

Choose a value form each interval

x_{1} = - 1 x_{2} = 1 x_{3} = 3

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is not a solution x_{2} = 1 x_{3} = 3

To determine if 0 < x < \frac{3}{2} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{3}{2} is the solution x_{3} = 3

To determine if x > \frac{3}{2} is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{3}{2} is the solution x > \frac{3}{2} is not a solution

Solution

0 < x < \frac{3}{2}

Alternative Form

x \in (0, \frac{3}{2})

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