Convert to Set Notation (x-7)(x+4)>0

$(x - 7) (x + 4) > 0$

Solve $x < - 4 or x > 7$ .

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

$x - 7 = 0$

$x + 4 = 0$

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

The final solution is all the values that make $(x - 7) (x + 4) > 0$ true.

$x = 7, - 4$

Use each root to create test intervals.

$x < - 4$

$- 4 < x < 7$

$x > 7$

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 $x < - 4$ to see if it makes the inequality true.

Choose a value on the interval $x < - 4$ and see if this value makes the original inequality true.

$x = - 6$

Replace $x$ with $- 6$ in the original inequality.

$((- 6) - 7) ((- 6) + 4) > 0$

The left side $26$ is greater than the right side $0$ , which means that the given statement is always true.

True

Test a value on the interval $- 4 < x < 7$ to see if it makes the inequality true.

Choose a value on the interval $- 4 < x < 7$ and see if this value makes the original inequality true.

$x = 0$

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

$((0) - 7) ((0) + 4) > 0$

The left side $- 28$ is not greater than the right side $0$ , which means that the given statement is false.

False

Test a value on the interval $x > 7$ to see if it makes the inequality true.

Choose a value on the interval $x > 7$ and see if this value makes the original inequality true.

$x = 10$

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

$((10) - 7) ((10) + 4) > 0$

The left side $42$ is greater than the right side $0$ , which means that the given statement is always true.

True

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

$x < - 4$ True

$- 4 < x < 7$ False

$x > 7$ True

$x < - 4$ True

$- 4 < x < 7$ False

$x > 7$ True

The solution consists of all of the true intervals.

$x < - 4$ or $x > 7$

Use the inequality $x < - 4 or x > 7$ to build the set notation.

${x | x < - 4 or x > 7}$

Convert to Set Notation (x-7)(x+4)>0

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