Solve the Inequality for x (x-8)(x+9)(7x+9)<0

$(x - 8) (x + 9) (7 x + 9) < 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 8 = 0$

$x + 9 = 0$

$7 x + 9 = 0$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

Set $7 x + 9$ equal to $0$ and solve for $x$ .

Set $7 x + 9$ equal to $0$ .

$7 x + 9 = 0$

Solve $7 x + 9 = 0$ for $x$ .

Subtract $9$ from both sides of the equation.

$7 x = - 9$

Divide each term in $7 x = - 9$ by $7$ and simplify.

Divide each term in $7 x = - 9$ by $7$ .

$\frac{7 x}{7} = \frac{- 9}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 9}{7}$

Divide $x$ by $1$ .

$x = \frac{- 9}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{9}{7}$

The final solution is all the values that make $(x - 8) (x + 9) (7 x + 9) < 0$ true.

$x = 8, - 9, - \frac{9}{7}$

Use each root to create test intervals.

$x < - 9$

$- 9 < x < - \frac{9}{7}$

$- \frac{9}{7} < x < 8$

$x > 8$

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

Test a value on the interval $x < - 9$ to see if it makes the inequality true.

Choose a value on the interval $x < - 9$ and see if this value makes the original inequality true.

$x = - 12$

Replace $x$ with $- 12$ in the original inequality.

$((- 12) - 8) ((- 12) + 9) (7 (- 12) + 9) < 0$

The left side $- 4500$ is less than the right side $0$ , which means that the given statement is always true.

True

Test a value on the interval $- 9 < x < - \frac{9}{7}$ to see if it makes the inequality true.

Choose a value on the interval $- 9 < x < - \frac{9}{7}$ and see if this value makes the original inequality true.

$x = - 5$

Replace $x$ with $- 5$ in the original inequality.

$((- 5) - 8) ((- 5) + 9) (7 (- 5) + 9) < 0$

The left side $1352$ is not less than the right side $0$ , which means that the given statement is false.

False

Test a value on the interval $- \frac{9}{7} < x < 8$ to see if it makes the inequality true.

Choose a value on the interval $- \frac{9}{7} < x < 8$ and see if this value makes the original inequality true.

$x = 0$

Replace $x$ with $0$ in the original inequality.

$((0) - 8) ((0) + 9) (7 (0) + 9) < 0$

The left side $- 648$ is less than the right side $0$ , which means that the given statement is always true.

True

Test a value on the interval $x > 8$ to see if it makes the inequality true.

Choose a value on the interval $x > 8$ and see if this value makes the original inequality true.

$x = 10$

Replace $x$ with $10$ in the original inequality.

$((10) - 8) ((10) + 9) (7 (10) + 9) < 0$

The left side $3002$ is not less than the right side $0$ , which means that the given statement is false.

False

Compare the intervals to determine which ones satisfy the original inequality.

$x < - 9$ True

$- 9 < x < - \frac{9}{7}$ False

$- \frac{9}{7} < x < 8$ True

$x > 8$ False

$x < - 9$ True

$- 9 < x < - \frac{9}{7}$ False

$- \frac{9}{7} < x < 8$ True

$x > 8$ False

The solution consists of all of the true intervals.

$x < - 9$ or $- \frac{9}{7} < x < 8$

The result can be shown in multiple forms.

Inequality Form:

$x < - 9 or - \frac{9}{7} < x < 8$

Interval Notation:

$(- \infty, - 9) \cup (- \frac{9}{7}, 8)$

Solve the Inequality for x (x-8)(x+9)(7x+9)<0

Related Questions

Support LCMGCF.com by disabling your adblocker.