Graph (x-1)(x-6)>=0

$(x - 1) (x - 6) \geq 0$

Step 1

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

$x - 1 = 0$

$x - 6 = 0$

Step 2

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 3

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Step 4

The final solution is all the values that make $(x - 1) (x - 6) \geq 0$ true.

$x = 1, 6$

Step 5

Use each root to create test intervals.

$x < 1$

$1 < x < 6$

$x > 6$

Step 6

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 $x < 1$ to see if it makes the inequality true.

Choose a value on the interval $x < 1$ and see if this value makes the original inequality true.

$x = 0$

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

$((0) - 1) ((0) - 6) \geq 0$

The left side $6$ is greater than the right side $0$ , which means that the given statement is always true.

True

Test a value on the interval $1 < x < 6$ to see if it makes the inequality true.

Choose a value on the interval $1 < x < 6$ and see if this value makes the original inequality true.

$x = 4$

Replace $x$ with $4$ in the original inequality.

$((4) - 1) ((4) - 6) \geq 0$

The left side $- 6$ is less than the right side $0$ , which means that the given statement is false.

False

Test a value on the interval $x > 6$ to see if it makes the inequality true.

Choose a value on the interval $x > 6$ and see if this value makes the original inequality true.

$x = 8$

Replace $x$ with $8$ in the original inequality.

$((8) - 1) ((8) - 6) \geq 0$

The left side $14$ 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.

$x < 1$ True

$1 < x < 6$ False

$x > 6$ True

$x < 1$ True

$1 < x < 6$ False

$x > 6$ True

Step 7

The solution consists of all of the true intervals.

$x \leq 1$ or $x \geq 6$

Step 8

Graph (x-1)(x-6)>=0

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