Solve 5x^2/4-x<2 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

\frac{- 2 11 + 2}{5} < x < \frac{2 11 + 2}{5}

Alternative Form

x \in (\frac{- 2 11 + 2}{5}, \frac{2 11 + 2}{5})

Evaluate

(5 \times \frac{x ^{2}}{4}) - x < 2

Multiply the terms

\frac{5 x ^{2}}{4} - x < 2

Multiply both sides of the inequality by 4

(\frac{5 x ^{2}}{4} - x) \times 4 < 2 \times 4

Multiply the terms

More Steps

5 x^{2} - 4 x < 2 \times 4

Multiply the terms

5 x^{2} - 4 x < 8

Move the expression to the left side

5 x^{2} - 4 x - 8 < 0

Rewrite the expression

5 x^{2} - 4 x - 8 = 0

Add or subtract both sides

5 x^{2} - 4 x = 8

Divide both sides

\frac{5 x ^{2} - 4 x}{5} = \frac{8}{5}

Evaluate

x^{2} - \frac{4}{5} x = \frac{8}{5}

Add the same value to both sides

x^{2} - \frac{4}{5} x + \frac{4}{25} = \frac{8}{5} + \frac{4}{25}

Simplify the expression

(x - \frac{2}{5})^{2} = \frac{44}{25}

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

x - \frac{2}{5} = \pm \frac{44}{25}

Simplify the expression

x - \frac{2}{5} = \pm \frac{2 11}{5}

Separate the equation into 2 possible cases

x - \frac{2}{5} = \frac{2 11}{5} x - \frac{2}{5} = - \frac{2 11}{5}

Solve the equation

More Steps

x = \frac{2 11 + 2}{5} x - \frac{2}{5} = - \frac{2 11}{5}

Solve the equation

More Steps

x = \frac{2 11 + 2}{5} x = \frac{- 2 11 + 2}{5}

Determine the test intervals using the critical values

x < \frac{- 2 11 + 2}{5} \frac{- 2 11 + 2}{5} < x < \frac{2 11 + 2}{5} x > \frac{2 11 + 2}{5}

Choose a value form each interval

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

To determine if x < \frac{- 2 11 + 2}{5} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < \frac{- 2 11 + 2}{5} is not a solution x_{2} = 0 x_{3} = 3

To determine if \frac{- 2 11 + 2}{5} < x < \frac{2 11 + 2}{5} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < \frac{- 2 11 + 2}{5} is not a solution \frac{- 2 11 + 2}{5} < x < \frac{2 11 + 2}{5} is the solution x_{3} = 3

To determine if x > \frac{2 11 + 2}{5} is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < \frac{- 2 11 + 2}{5} is not a solution \frac{- 2 11 + 2}{5} < x < \frac{2 11 + 2}{5} is the solution x > \frac{2 11 + 2}{5} is not a solution

Solution

\frac{- 2 11 + 2}{5} < x < \frac{2 11 + 2}{5}

Alternative Form

x \in (\frac{- 2 11 + 2}{5}, \frac{2 11 + 2}{5})

Show Solution