Solve |x^4| > 3 - ScanMath

Evaluate

x^{4} > 3

When the expression in absolute value bars is not negative, remove the bars

x^{4} > 3

Move the expression to the left side

x^{4} - 3 > 0

Rewrite the expression

x^{4} - 3 = 0

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

x^{4} = 0 + 3

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

x^{4} = 3

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

x = \pm 43

Separate the equation into 2 possible cases

x = 43 x = - 43

Determine the test intervals using the critical values

x < - 43 - 43 < x < 43 x > 43

Choose a value form each interval

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

To determine if x < - 43 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 43 is the solution x_{2} = 0 x_{3} = 2

To determine if - 43 < x < 43 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 43 is the solution - 43 < x < 43 is not a solution x_{3} = 2

To determine if x > 43 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 43 is the solution - 43 < x < 43 is not a solution x > 43 is the solution

Solution

x \in (- \infty, - 43) \cup (43, + \infty)

Solve the inequality