Solve m < 3m^2 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for m

m \in (- \infty, 0) \cup (\frac{1}{3}, + \infty)

Evaluate

m < 3 m^{2}

Move the expression to the left side

m - 3 m^{2} < 0

Rewrite the expression

m - 3 m^{2} = 0

Factor the expression

More Steps

m (1 - 3 m) = 0

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

m = 0 1 - 3 m = 0

Solve the equation for m

More Steps

m = 0 m = \frac{1}{3}

Determine the test intervals using the critical values

m < 0 0 < m < \frac{1}{3} m > \frac{1}{3}

Choose a value form each interval

m_{1} = - 1 m_{2} = \frac{1}{6} m_{3} = 2

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

More Steps

m < 0 is the solution m_{2} = \frac{1}{6} m_{3} = 2

To determine if 0 < m < \frac{1}{3} is the solution to the inequality,test if the chosen value m = \frac{1}{6} satisfies the initial inequality

More Steps

m < 0 is the solution 0 < m < \frac{1}{3} is not a solution m_{3} = 2

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

More Steps

m < 0 is the solution 0 < m < \frac{1}{3} is not a solution m > \frac{1}{3} is the solution

Solution

m \in (- \infty, 0) \cup (\frac{1}{3}, + \infty)

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