Solve 3 I< I-I^4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

- 32 < I < 0

Alternative Form

I \in (- 32, 0)

Evaluate

3 I < I - I^{4}

Move the expression to the left side

3 I - (I - I^{4}) < 0

Subtract the terms

More Steps

2 I + I^{4} < 0

Rewrite the expression

2 I + I^{4} = 0

Factor the expression

I (2 + I^{3}) = 0

Separate the equation into 2 possible cases

I = 0 2 + I^{3} = 0

Solve the equation

More Steps

I = 0 I = - 32

Determine the test intervals using the critical values

I < - 32 - 32 < I < 0 I > 0

Choose a value form each interval

I_{1} = - 2 I_{2} = - 1 I_{3} = 1

To determine if I < - 32 is the solution to the inequality,test if the chosen value I = - 2 satisfies the initial inequality

More Steps

I < - 32 is not a solution I_{2} = - 1 I_{3} = 1

To determine if - 32 < I < 0 is the solution to the inequality,test if the chosen value I = - 1 satisfies the initial inequality

More Steps

I < - 32 is not a solution - 32 < I < 0 is the solution I_{3} = 1

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

More Steps

I < - 32 is not a solution - 32 < I < 0 is the solution I > 0 is not a solution

Solution

- 32 < I < 0

Alternative Form

I \in (- 32, 0)

Show Solution