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. )
Step 2: Replace the inequality with the equal sign and solve all the roots.
Step 3: Mark each root in turn from left to right on the number axis.
Step 4: Draw a line through the root: Draw a line from the upper right corner to the lower left corner of the rightmost root based on the number axis, and then pass up through the second right heel, passing through each root one by one.
Step 5: Observe the inequality. If the inequality is ">", take the range above the number axis and within the heel line; If the inequality symbol is "
It can be simply written as a secret recipe: "from top to bottom, from right to left, odd numbers pass, even numbers pass."
Extended data:
"Needle-piercing method" is also called "multi-axis root-piercing method" or "using several threads".
To be precise, it should be called "ordinal axis marking method". Ordinal axis: the number axis that omits the origin and unit and only represents the size of the number. Of the two points marked on the sequence axis, the left point represents a smaller number than the right point.
When the higher inequality f (x) >; 0 (or
In order to vividly reflect the changing law of the current negative value, a wavy line can be drawn from the upper right to pass through each corresponding point in turn, and the direction will remain unchanged after passing through the last point. This kind of painting is commonly known as "threading the needle".
Reference: threading the needle-Baidu Encyclopedia