This applet shows a number line with two points on it.
You can move the points anywhere on the line. Note when A is less than B or A is greater than B.
The different rules for operating on both sides of an inequality are shown. By checking a box you can explore the results of

add a value to both sides, c

multiplying both sides by a positive number, pm

multiplying both sides by a negative number, nm

raise both sides to a positive exponent, pe

raise both sides to a negative exponent, ne

For each rule can can change the value with the slider.
The results are shown with different symbols for each type of operation. The red symbol correspond to the A point and the green symbol correspond to the B point.

Check the rules out one at a time.
For each rule notice whether the modified points are in the same order or reversed order.
Explain the rules for operating on both sides of an inequality.