Solve 15t^4>4(5t 16)

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

t \in (- \infty, 0) \cup (\frac{4 3 9}{3}, + \infty)

Evaluate

15 t^{4} > 4 (5 t \times 16)

Remove the parentheses

15 t^{4} > 4 \times 5 t \times 16

Multiply the terms

More Steps

15 t^{4} > 320 t

Move the expression to the left side

15 t^{4} - 320 t > 0

Rewrite the expression

15 t^{4} - 320 t = 0

Factor the expression

5 t (3 t^{3} - 64) = 0

Divide both sides

t (3 t^{3} - 64) = 0

Separate the equation into 2 possible cases

t = 0 3 t^{3} - 64 = 0

Solve the equation

More Steps

t = 0 t = \frac{4 3 9}{3}

Determine the test intervals using the critical values

t < 0 0 < t < \frac{4 3 9}{3} t > \frac{4 3 9}{3}

Choose a value form each interval

t_{1} = - 1 t_{2} = 1 t_{3} = 4

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

More Steps

t < 0 is the solution t_{2} = 1 t_{3} = 4

To determine if 0 < t < \frac{4 3 9}{3} is the solution to the inequality,test if the chosen value t = 1 satisfies the initial inequality

More Steps

t < 0 is the solution 0 < t < \frac{4 3 9}{3} is not a solution t_{3} = 4

To determine if t > \frac{4 3 9}{3} is the solution to the inequality,test if the chosen value t = 4 satisfies the initial inequality

More Steps

t < 0 is the solution 0 < t < \frac{4 3 9}{3} is not a solution t > \frac{4 3 9}{3} is the solution

Solution

t \in (- \infty, 0) \cup (\frac{4 3 9}{3}, + \infty)

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