Solve 10\ge2x^4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- 45 \leq x \leq 45

Alternative Form

x \in [- 45, 45]

Evaluate

10 \geq 2 x^{4}

Move the expression to the left side

10 - 2 x^{4} \geq 0

Rewrite the expression

10 - 2 x^{4} = 0

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

- 2 x^{4} = 0 - 10

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

- 2 x^{4} = - 10

Change the signs on both sides of the equation

2 x^{4} = 10

Divide both sides

\frac{2 x ^{4}}{2} = \frac{10}{2}

Divide the numbers

x^{4} = \frac{10}{2}

Divide the numbers

More Steps

x^{4} = 5

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

x = \pm 45

Separate the equation into 2 possible cases

x = 45 x = - 45

Determine the test intervals using the critical values

x < - 45 - 45 < x < 45 x > 45

Choose a value form each interval

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

To determine if x < - 45 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 45 is not a solution x_{2} = 0 x_{3} = 2

To determine if - 45 < x < 45 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 45 is not a solution - 45 < x < 45 is the solution x_{3} = 2

To determine if x > 45 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 45 is not a solution - 45 < x < 45 is the solution x > 45 is not a solution

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

- 45 \leq x \leq 45 is the solution

Solution

- 45 \leq x \leq 45

Alternative Form

x \in [- 45, 45]

Show Solution