Solve x^2 - 2 < 7/2x

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

- \frac{1}{2} < x < 4

Alternative Form

x \in (- \frac{1}{2}, 4)

Evaluate

x^{2} - 2 < \frac{7}{2} x

Move the expression to the left side

x^{2} - 2 - \frac{7}{2} x < 0

Rewrite the expression

x^{2} - 2 - \frac{7}{2} x = 0

Factor the expression

More Steps

\frac{1}{2} (x - 4) (2 x + 1) = 0

Divide the terms

(x - 4) (2 x + 1) = 0

When the product of factors equals 0,at least one factor is 0

x - 4 = 0 2 x + 1 = 0

Solve the equation for x

More Steps

x = 4 2 x + 1 = 0

Solve the equation for x

More Steps

x = 4 x = - \frac{1}{2}

Determine the test intervals using the critical values

x < - \frac{1}{2} - \frac{1}{2} < x < 4 x > 4

Choose a value form each interval

x_{1} = - 2 x_{2} = 2 x_{3} = 5

To determine if x < - \frac{1}{2} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{1}{2} is not a solution x_{2} = 2 x_{3} = 5

To determine if - \frac{1}{2} < x < 4 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - \frac{1}{2} is not a solution - \frac{1}{2} < x < 4 is the solution x_{3} = 5

To determine if x > 4 is the solution to the inequality,test if the chosen value x = 5 satisfies the initial inequality

More Steps

x < - \frac{1}{2} is not a solution - \frac{1}{2} < x < 4 is the solution x > 4 is not a solution

Solution

- \frac{1}{2} < x < 4

Alternative Form

x \in (- \frac{1}{2}, 4)

Show Solution