Solve x x-1<4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- 5 < x < 5

Alternative Form

x \in (- 5, 5)

Evaluate

x \times x - 1 < 4

Multiply the terms

x^{2} - 1 < 4

Move the expression to the left side

x^{2} - 1 - 4 < 0

Subtract the numbers

x^{2} - 5 < 0

Rewrite the expression

x^{2} - 5 = 0

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

x^{2} = 0 + 5

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

x^{2} = 5

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

x = \pm 5

Separate the equation into 2 possible cases

x = 5 x = - 5

Determine the test intervals using the critical values

x < - 5 - 5 < x < 5 x > 5

Choose a value form each interval

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

To determine if x < - 5 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 5 is not a solution x_{2} = 0 x_{3} = 3

To determine if - 5 < x < 5 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 5 is not a solution - 5 < x < 5 is the solution x_{3} = 3

To determine if x > 5 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < - 5 is not a solution - 5 < x < 5 is the solution x > 5 is not a solution

Solution

- 5 < x < 5

Alternative Form

x \in (- 5, 5)

Show Solution