Solve -1c^41≥-14

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for c

- 414 \leq c \leq 414

Alternative Form

c \in [- 414, 414]

Evaluate

- c^{4} \times 1 \geq - 14

Any expression multiplied by 1 remains the same

- c^{4} \geq - 14

Move the expression to the left side

- c^{4} - (- 14) \geq 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

- c^{4} + 14 \geq 0

Rewrite the expression

- c^{4} + 14 = 0

Move the constant to the right-hand side and change its sign

- c^{4} = 0 - 14

Removing 0 doesn't change the value,so remove it from the expression

- c^{4} = - 14

Change the signs on both sides of the equation

c^{4} = 14

Take the root of both sides of the equation and remember to use both positive and negative roots

c = \pm 414

Separate the equation into 2 possible cases

c = 414 c = - 414

Determine the test intervals using the critical values

c < - 414 - 414 < c < 414 c > 414

Choose a value form each interval

c_{1} = - 3 c_{2} = 0 c_{3} = 3

To determine if c < - 414 is the solution to the inequality,test if the chosen value c = - 3 satisfies the initial inequality

More Steps

c < - 414 is not a solution c_{2} = 0 c_{3} = 3

To determine if - 414 < c < 414 is the solution to the inequality,test if the chosen value c = 0 satisfies the initial inequality

More Steps

c < - 414 is not a solution - 414 < c < 414 is the solution c_{3} = 3

To determine if c > 414 is the solution to the inequality,test if the chosen value c = 3 satisfies the initial inequality

More Steps

c < - 414 is not a solution - 414 < c < 414 is the solution c > 414 is not a solution

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

- 414 \leq c \leq 414 is the solution

Solution

- 414 \leq c \leq 414

Alternative Form

c \in [- 414, 414]

Show Solution