Solve r1 < r^2 - ScanMath

Evaluate

r \times 1 < r^{2}

Any expression multiplied by 1 remains the same

r < r^{2}

Move the expression to the left side

r - r^{2} < 0

Rewrite the expression

r - r^{2} = 0

Factor the expression

More Steps

r (1 - r) = 0

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

r = 0 1 - r = 0

Solve the equation for r

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r = 0 r = 1

Determine the test intervals using the critical values

r < 0 0 < r < 1 r > 1

Choose a value form each interval

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

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

More Steps

r < 0 is the solution r_{2} = \frac{1}{2} r_{3} = 2

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

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r < 0 is the solution 0 < r < 1 is not a solution r_{3} = 2

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

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

Solution

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

Solve the inequality