Solve -7(4 x) 9x>-9

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- \frac{7}{14} < x < \frac{7}{14}

Alternative Form

x \in (- \frac{7}{14}, \frac{7}{14})

Evaluate

- 7 \times 4 x \times 9 x > - 9

Multiply

More Steps

- 252 x^{2} > - 9

Move the expression to the left side

- 252 x^{2} - (- 9) > 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 252 x^{2} + 9 > 0

Rewrite the expression

- 252 x^{2} + 9 = 0

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

- 252 x^{2} = 0 - 9

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

- 252 x^{2} = - 9

Change the signs on both sides of the equation

252 x^{2} = 9

Divide both sides

\frac{252 x ^{2}}{252} = \frac{9}{252}

Divide the numbers

x^{2} = \frac{9}{252}

Cancel out the common factor 9

x^{2} = \frac{1}{28}

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

x = \pm \frac{1}{28}

Simplify the expression

More Steps

x = \pm \frac{7}{14}

Separate the equation into 2 possible cases

x = \frac{7}{14} x = - \frac{7}{14}

Determine the test intervals using the critical values

x < - \frac{7}{14} - \frac{7}{14} < x < \frac{7}{14} x > \frac{7}{14}

Choose a value form each interval

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

To determine if x < - \frac{7}{14} is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - \frac{7}{14} is not a solution x_{2} = 0 x_{3} = 1

To determine if - \frac{7}{14} < x < \frac{7}{14} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{7}{14} is not a solution - \frac{7}{14} < x < \frac{7}{14} is the solution x_{3} = 1

To determine if x > \frac{7}{14} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < - \frac{7}{14} is not a solution - \frac{7}{14} < x < \frac{7}{14} is the solution x > \frac{7}{14} is not a solution

Solution

- \frac{7}{14} < x < \frac{7}{14}

Alternative Form

x \in (- \frac{7}{14}, \frac{7}{14})

Show Solution