Solve the Inequality for y (y-2)(y-4)>0

$(y - 2) (y - 4) > 0$

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

$y - 2 = 0$

$y - 4 = 0$

Set $y - 2$ equal to $0$ and solve for $y$ .

Set $y - 2$ equal to $0$ .

$y - 2 = 0$

Add $2$ to both sides of the equation.

$y = 2$

Set $y - 4$ equal to $0$ and solve for $y$ .

Set $y - 4$ equal to $0$ .

$y - 4 = 0$

Add $4$ to both sides of the equation.

$y = 4$

The final solution is all the values that make $(y - 2) (y - 4) > 0$ true.

$y = 2, 4$

Use each root to create test intervals.

$y < 2$

$2 < y < 4$

$y > 4$

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 $y < 2$ to see if it makes the inequality true.

Choose a value on the interval $y < 2$ and see if this value makes the original inequality true.

$y = 0$

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

$((0) - 2) ((0) - 4) > 0$

The left side $8$ is greater than the right side $0$ , which means that the given statement is always true.

True

Test a value on the interval $2 < y < 4$ to see if it makes the inequality true.

Choose a value on the interval $2 < y < 4$ and see if this value makes the original inequality true.

$y = 3$

Replace $y$ with $3$ in the original inequality.

$((3) - 2) ((3) - 4) > 0$

The left side $- 1$ is not greater than the right side $0$ , which means that the given statement is false.

False

Test a value on the interval $y > 4$ to see if it makes the inequality true.

Choose a value on the interval $y > 4$ and see if this value makes the original inequality true.

$y = 6$

Replace $y$ with $6$ in the original inequality.

$((6) - 2) ((6) - 4) > 0$

The left side $8$ 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.

$y < 2$ True

$2 < y < 4$ False

$y > 4$ True

$y < 2$ True

$2 < y < 4$ False

$y > 4$ True

The solution consists of all of the true intervals.

$y < 2$ or $y > 4$

The result can be shown in multiple forms.

Inequality Form:

$y < 2 or y > 4$

Interval Notation:

$(- \infty, 2) \cup (4, \infty)$

Solve the Inequality for y (y-2)(y-4)>0

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