Solve 2x^4<=14 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- 47 \leq x \leq 47

Alternative Form

x \in [- 47, 47]

Evaluate

2 x^{4} \leq 14

Move the expression to the left side

2 x^{4} - 14 \leq 0

Rewrite the expression

2 x^{4} - 14 = 0

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

2 x^{4} = 0 + 14

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

2 x^{4} = 14

Divide both sides

\frac{2 x ^{4}}{2} = \frac{14}{2}

Divide the numbers

x^{4} = \frac{14}{2}

Divide the numbers

More Steps

x^{4} = 7

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

x = \pm 47

Separate the equation into 2 possible cases

x = 47 x = - 47

Determine the test intervals using the critical values

x < - 47 - 47 < x < 47 x > 47

Choose a value form each interval

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

To determine if x < - 47 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 47 is not a solution x_{2} = 0 x_{3} = 3

To determine if - 47 < x < 47 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 47 is not a solution - 47 < x < 47 is the solution x_{3} = 3

To determine if x > 47 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < - 47 is not a solution - 47 < x < 47 is the solution x > 47 is not a solution

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

- 47 \leq x \leq 47 is the solution

Solution

- 47 \leq x \leq 47

Alternative Form

x \in [- 47, 47]

Show Solution