Solve x1<x^2 - ScanMath

Evaluate

x \times 1 < x^{2}

Any expression multiplied by 1 remains the same

x < x^{2}

Move the expression to the left side

x - x^{2} < 0

Rewrite the expression

x - x^{2} = 0

Factor the expression

More Steps

x (1 - x) = 0

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

x = 0 1 - x = 0

Solve the equation for x

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x = 0 x = 1

Determine the test intervals using the critical values

x < 0 0 < x < 1 x > 1

Choose a value form each interval

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

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

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x < 0 is the solution x_{2} = \frac{1}{2} x_{3} = 2

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

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

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

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x < 0 is the solution 0 < x < 1 is not a solution x > 1 is the solution

Solution

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

Solve the inequality