Solve -5n^2(-3n-1)≥ n-95n

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

n \geq 0

Alternative Form

n \in [0, + \infty)

Evaluate

- 5 n^{2} (- 3 n - 1) \geq n - 95 n

Subtract the terms

More Steps

- 5 n^{2} (- 3 n - 1) \geq - 94 n

Move the expression to the left side

- 5 n^{2} (- 3 n - 1) - (- 94 n) \geq 0

Subtract the terms

More Steps

15 n^{3} + 5 n^{2} + 94 n \geq 0

Rewrite the expression

15 n^{3} + 5 n^{2} + 94 n = 0

Factor the expression

n (15 n^{2} + 5 n + 94) = 0

Separate the equation into 2 possible cases

n = 0 15 n^{2} + 5 n + 94 = 0

Solve the equation

More Steps

n = 0 n \in / R

Find the union

n = 0

Determine the test intervals using the critical values

n < 0 n > 0

Choose a value form each interval

n_{1} = - 1 n_{2} = 1

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

More Steps

n < 0 is not a solution n_{2} = 1

To determine if n > 0 is the solution to the inequality,test if the chosen value n = 1 satisfies the initial inequality

More Steps

n < 0 is not a solution n > 0 is the solution

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

n \geq 0 is the solution

Solution

n \geq 0

Alternative Form

n \in [0, + \infty)

Show Solution