Solve 7 - 2(x 1) < 3x^4

Question

Solve the inequality

x \in (- \infty, - 1.340278) \cup (1.122086, + \infty)

Evaluate

7 - 2 (x \times 1) < 3 x^{4}

Remove the parentheses

7 - 2 x \times 1 < 3 x^{4}

Multiply the terms

7 - 2 x < 3 x^{4}

Move the expression to the left side

7 - 2 x - 3 x^{4} < 0

Rewrite the expression

7 - 2 x - 3 x^{4} = 0

Find the critical values by solving the corresponding equation

x \approx - 1.340278 x \approx 1.122086

Determine the test intervals using the critical values

x < - 1.340278 - 1.340278 < x < 1.122086 x > 1.122086

Choose a value form each interval

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

To determine if x < - 1.340278 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 1.340278 is the solution x_{2} = 0 x_{3} = 2

To determine if - 1.340278 < x < 1.122086 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 1.340278 is the solution - 1.340278 < x < 1.122086 is not a solution x_{3} = 2

To determine if x > 1.122086 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 1.340278 is the solution - 1.340278 < x < 1.122086 is not a solution x > 1.122086 is the solution

Solution

x \in (- \infty, - 1.340278) \cup (1.122086, + \infty)

Show Solution