Solve 2-x/43x-x^2<0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \in (- \infty, - \frac{946}{22}) \cup (\frac{946}{22}, + \infty)

Evaluate

2 - \frac{x}{43} x - x^{2} < 0

Multiply the terms

More Steps

2 - \frac{x ^{2}}{43} - x^{2} < 0

Multiply both sides of the inequality by 43

(2 - \frac{x ^{2}}{43} - x^{2}) \times 43 < 0 \times 43

Multiply the terms

More Steps

86 - x^{2} - 43 x^{2} < 0 \times 43

Multiply the terms

86 - x^{2} - 43 x^{2} < 0

Rewrite the expression

86 - x^{2} - 43 x^{2} = 0

Simplify

More Steps

86 - 44 x^{2} = 0

Rewrite the expression

- 44 x^{2} = - 86

Change the signs on both sides of the equation

44 x^{2} = 86

Divide both sides

\frac{44 x ^{2}}{44} = \frac{86}{44}

Divide the numbers

x^{2} = \frac{86}{44}

Cancel out the common factor 2

x^{2} = \frac{43}{22}

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

x = \pm \frac{43}{22}

Simplify the expression

More Steps

x = \pm \frac{946}{22}

Separate the equation into 2 possible cases

x = \frac{946}{22} x = - \frac{946}{22}

Determine the test intervals using the critical values

x < - \frac{946}{22} - \frac{946}{22} < x < \frac{946}{22} x > \frac{946}{22}

Choose a value form each interval

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

To determine if x < - \frac{946}{22} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{946}{22} is the solution x_{2} = 0 x_{3} = 2

To determine if - \frac{946}{22} < x < \frac{946}{22} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{946}{22} is the solution - \frac{946}{22} < x < \frac{946}{22} is not a solution x_{3} = 2

To determine if x > \frac{946}{22} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - \frac{946}{22} is the solution - \frac{946}{22} < x < \frac{946}{22} is not a solution x > \frac{946}{22} is the solution

Solution

x \in (- \infty, - \frac{946}{22}) \cup (\frac{946}{22}, + \infty)

Show Solution