Solve x-4-(x^2)<-3(x^4)

Question

Solve the inequality

- 1.223384 < x < 1.080353

Alternative Form

x \in (- 1.223384, 1.080353)

Evaluate

x - 4 - x^{2} < - 3 x^{4}

Move the expression to the left side

x - 4 - x^{2} - (- 3 x^{4}) < 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

x - 4 - x^{2} + 3 x^{4} < 0

Rewrite the expression

x - 4 - x^{2} + 3 x^{4} = 0

Find the critical values by solving the corresponding equation

x \approx 1.080353 x \approx - 1.223384

Determine the test intervals using the critical values

x < - 1.223384 - 1.223384 < x < 1.080353 x > 1.080353

Choose a value form each interval

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

To determine if x < - 1.223384 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 1.223384 is not a solution x_{2} = 0 x_{3} = 2

To determine if - 1.223384 < x < 1.080353 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 1.223384 is not a solution - 1.223384 < x < 1.080353 is the solution x_{3} = 2

To determine if x > 1.080353 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 1.223384 is not a solution - 1.223384 < x < 1.080353 is the solution x > 1.080353 is not a solution

Solution

- 1.223384 < x < 1.080353

Alternative Form

x \in (- 1.223384, 1.080353)

Show Solution