(x+6)(x-1)>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+6=0
x-1=0
Set the first factor equal to 0.
x+6=0
Subtract 6 from both sides of the equation.
x=-6
x=-6
Set the next factor equal to 0.
x-1=0
Add 1 to both sides of the equation.
x=1
x=1
Consolidate the solutions.
x=-6,1
Use each root to create test intervals.
x<-6
-6<x<1
x>1
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)+6)((-8)-1)>0
The left side 18 is greater than the right side 0, which means that the given statement is always true.
True
True
Test a value on the interval -6<x<1 to see if it makes the inequality true.
Choose a value on the interval -6<x<1 and see if this value makes the original inequality true.
x=0
Replace x with 0 in the original inequality.
((0)+6)((0)-1)>0
The left side -6 is not greater than the right side 0, which means that the given statement is false.
False
False
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=4
Replace x with 4 in the original inequality.
((4)+6)((4)-1)>0
The left side 30 is greater than the right side 0, which means that the given statement is always true.
True
True
Compare the intervals to determine which ones satisfy the original inequality.
x<-6 True
-6<x<1 False
x>1 True
x<-6 True
-6<x<1 False
x>1 True
The solution consists of all of the true intervals.
x<-6 or x>1
The result can be shown in multiple forms.
Inequality Form:
x<-6 or x>1
Interval Notation:
(-∞,-6)∪(1,∞)
<div data-graph-input="{"graphs":[{"ascii":"x1","color":0,"isGrey":false,"dashed":false,"holes":[]}],"asymptotes":[],"segments":[],"areaBetweenCurves":[],"points":[],"HasGraphInput":true}” class=”GraphWrapper”>
