Solve x^2<2x - ScanMath

Evaluate

x^{2} < 2 x

Move the expression to the left side

x^{2} - 2 x < 0

Rewrite the expression

x^{2} - 2 x = 0

Factor the expression

More Steps

x (x - 2) = 0

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

x = 0 x - 2 = 0

Solve the equation for x

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x = 0 x = 2

Determine the test intervals using the critical values

x < 0 0 < x < 2 x > 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 < 2 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

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

To determine if x > 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 < 2 is the solution x > 2 is not a solution

Solution

0 < x < 2

Alternative Form

x \in (0, 2)

Solve the inequality