Solve 12t-2 < -5t^36

Evaluate

12 t - 2 < - 5 t^{3} \times 6

Multiply the terms

12 t - 2 < - 30 t^{3}

Move the expression to the left side

12 t - 2 - (- 30 t^{3}) < 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

12 t - 2 + 30 t^{3} < 0

Rewrite the expression

12 t - 2 + 30 t^{3} = 0

Factor the expression

2 (6 t - 1 + 15 t^{3}) = 0

Divide both sides

6 t - 1 + 15 t^{3} = 0

Calculate

t \approx 0.156993

Determine the test intervals using the critical values

t < 0.156993 t > 0.156993

Choose a value form each interval

t_{1} = - 1 t_{2} = 1

To determine if t < 0.156993 is the solution to the inequality,test if the chosen value t = - 1 satisfies the initial inequality

More Steps

t < 0.156993 is the solution t_{2} = 1

To determine if t > 0.156993 is the solution to the inequality,test if the chosen value t = 1 satisfies the initial inequality

More Steps

t < 0.156993 is the solution t > 0.156993 is not a solution

Solution

t < 0.156993

Alternative Form

t \in (- \infty, 0.156993)

Solve the inequality