Solve 5x^2<1 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- \frac{5}{5} < x < \frac{5}{5}

Alternative Form

x \in (- \frac{5}{5}, \frac{5}{5})

Evaluate

5 x^{2} < 1

Move the expression to the left side

5 x^{2} - 1 < 0

Rewrite the expression

5 x^{2} - 1 = 0

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

5 x^{2} = 0 + 1

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

5 x^{2} = 1

Divide both sides

\frac{5 x ^{2}}{5} = \frac{1}{5}

Divide the numbers

x^{2} = \frac{1}{5}

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

x = \pm \frac{1}{5}

Simplify the expression

More Steps

x = \pm \frac{5}{5}

Separate the equation into 2 possible cases

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

Determine the test intervals using the critical values

x < - \frac{5}{5} - \frac{5}{5} < x < \frac{5}{5} x > \frac{5}{5}

Choose a value form each interval

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

To determine if x < - \frac{5}{5} is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - \frac{5}{5} is not a solution x_{2} = 0 x_{3} = 1

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

More Steps

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

To determine if x > \frac{5}{5} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

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

Solution

- \frac{5}{5} < x < \frac{5}{5}

Alternative Form

x \in (- \frac{5}{5}, \frac{5}{5})

Show Solution