You are lucky to live exactly halfway between two branches of your favorite pizza restaurant. One is 5 miles to the west of your house and the other is 5 miles to the east.
All things being equal, does it matter which restaurant you visit when you crave a slice of pizza? No, because 5 miles is 5 miles, whether it is east or west. Sometimes, direction just doesn’t matter.
The same is true in mathematics; sometimes it just doesn’t matter whether a point lies 5 units to the left of zero or 5 units to the right. For these circumstances, the notion of absolute value is useful.
This tool gives you the opportunity to experiment with absolute value inequalities involving expressions of the form the absolute value of a x plus b.
You can determine the sense and strictness of the inequality you want to solve by choosing one of the four inequality symbols from the drop down list.
The solution is presented in interval notation and graphed on the number line.
Also, a more illuminating graph is supplied that better shows the relationship between the left side of the inequality and the right side.
You can adjust the values of the parameters a, b, and c by using slider controls or by typing values directly into the inequality.
There are many different situations using combinations of values for the three parameters and the four inequality symbols.
Try to think of as many as you can as you use this tool to learn about expressions that compare the absolute value of a x plus b to c. Remember not to forget about negative number! 1