Solve 5x<3x^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 x

x \in (- \infty, 0) \cup (\frac{5}{3}, + \infty)

Evaluate

5 x < 3 x^{2}

Move the expression to the left side

5 x - 3 x^{2} < 0

Rewrite the expression

5 x - 3 x^{2} = 0

Factor the expression

More Steps

x (5 - 3 x) = 0

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

x = 0 5 - 3 x = 0

Solve the equation for x

More Steps

x = 0 x = \frac{5}{3}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{5}{3} x > \frac{5}{3}

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 the solution x_{2} = 1 x_{3} = 3

To determine if 0 < x < \frac{5}{3} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < \frac{5}{3} is not a solution x_{3} = 3

To determine if x > \frac{5}{3} is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < \frac{5}{3} is not a solution x > \frac{5}{3} is the solution

Solution

x \in (- \infty, 0) \cup (\frac{5}{3}, + \infty)

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