Step 1: Through many properties of inequality, move the terms of inequality to make the right side 0. (Note: Make sure that the coefficient before x is positive. )
Such as x3-2x2-x+2 >; 0 to (x-2)(x- 1)(x+ 1)>0.
Step 2: Replace the inequality with the equal sign and solve all the roots.
For example, the root of (x-2)(x- 1)(x+ 1)=0 is: x 1=2, x2= 1, x3=- 1.
Step 3: Mark each root in turn from left to right on the number axis.
For example:-1 1 2
Step 3: Draw a line through the root: based on the number axis, pass through the root from the upper left of the rightmost root, to the lower right, and then go up through the second rightmost root, and pass through each root one by one.
Step 4: Observe the inequality. If the inequality is ">", take the range above the number axis and within the heel line; If the inequality symbol is "
For example:
The root of if (x-2) (x-1) (x+1) > 0.
Mark root on the number axis:-1 1 2
Draw a line: cross the root from the top right.
Because it is not equal to ">" to take the range above the number axis and within the heel line. Namely:-1
Odd-even-opacity means that if two solutions are the same number, the number should be crossed by two numbers, such as (x- 1) = 0, so don't cross 1 when the two solutions cross.