Solve (x^2)*(4-3x) >= 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \leq \frac{4}{3}

Alternative Form

x \in (- \infty, \frac{4}{3}]

Evaluate

x^{2} (4 - 3 x) \geq 0

Rewrite the expression

x^{2} (4 - 3 x) = 0

Separate the equation into 2 possible cases

x^{2} = 0 4 - 3 x = 0

The only way a power can be 0 is when the base equals 0

x = 0 4 - 3 x = 0

Solve the equation

More Steps

x = 0 x = \frac{4}{3}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{4}{3} x > \frac{4}{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{4}{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{4}{3} is the solution x_{3} = 3

To determine if x > \frac{4}{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{4}{3} is the solution x > \frac{4}{3} is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

x \leq 0 is the solution 0 \leq x \leq \frac{4}{3} is the solution

Solution

x \leq \frac{4}{3}

Alternative Form

x \in (- \infty, \frac{4}{3}]

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