Solve 43x^43 < 41

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- \frac{4 41 \times 12 9 ^{3}}{129} < x < \frac{4 41 \times 12 9 ^{3}}{129}

Alternative Form

x \in (- \frac{4 41 \times 12 9 ^{3}}{129}, \frac{4 41 \times 12 9 ^{3}}{129})

Evaluate

43 x^{4} \times 3 < 41

Multiply the terms

129 x^{4} < 41

Move the expression to the left side

129 x^{4} - 41 < 0

Rewrite the expression

129 x^{4} - 41 = 0

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

129 x^{4} = 0 + 41

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

129 x^{4} = 41

Divide both sides

\frac{129 x ^{4}}{129} = \frac{41}{129}

Divide the numbers

x^{4} = \frac{41}{129}

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

x = \pm 4 \frac{41}{129}

Simplify the expression

More Steps

x = \pm \frac{4 41 \times 12 9 ^{3}}{129}

Separate the equation into 2 possible cases

x = \frac{4 41 \times 12 9 ^{3}}{129} x = - \frac{4 41 \times 12 9 ^{3}}{129}

Determine the test intervals using the critical values

x < - \frac{4 41 \times 12 9 ^{3}}{129} - \frac{4 41 \times 12 9 ^{3}}{129} < x < \frac{4 41 \times 12 9 ^{3}}{129} x > \frac{4 41 \times 12 9 ^{3}}{129}

Choose a value form each interval

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

To determine if x < - \frac{4 41 \times 12 9 ^{3}}{129} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{4 41 \times 12 9 ^{3}}{129} is not a solution x_{2} = 0 x_{3} = 2

To determine if - \frac{4 41 \times 12 9 ^{3}}{129} < x < \frac{4 41 \times 12 9 ^{3}}{129} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{4 41 \times 12 9 ^{3}}{129} is not a solution - \frac{4 41 \times 12 9 ^{3}}{129} < x < \frac{4 41 \times 12 9 ^{3}}{129} is the solution x_{3} = 2

To determine if x > \frac{4 41 \times 12 9 ^{3}}{129} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - \frac{4 41 \times 12 9 ^{3}}{129} is not a solution - \frac{4 41 \times 12 9 ^{3}}{129} < x < \frac{4 41 \times 12 9 ^{3}}{129} is the solution x > \frac{4 41 \times 12 9 ^{3}}{129} is not a solution

Solution

- \frac{4 41 \times 12 9 ^{3}}{129} < x < \frac{4 41 \times 12 9 ^{3}}{129}

Alternative Form

x \in (- \frac{4 41 \times 12 9 ^{3}}{129}, \frac{4 41 \times 12 9 ^{3}}{129})

Show Solution