Graphing inequalities
graphing inequalities is what this lesson will teach you.
An inequality is basically any mathematical statement that uses greater than (>), less than (<), less than or equal (≤), greater than or equal (≥), or not equal (≠)symbol.
For example, the statement x > 6 is an inequality
Example #1
Graph x > 2
Draw a non-shaded or open circle at 2 and shade everything on the right of 2.
The shaded area in red is your solution. It means that the solution can be any number on the right of 2.
Notice that 2 is not shaded because 2 is not included in your solution.
Notice also that although the last number on the number line is 9, your solution does not stop at 9.
Any other number bigger than 9 is a solution
In fact, the solution is infinite, so it would be very silly trying to graph all solutions to this problem.
Example #2
Graph x < -3
Draw an open circle at -3 and shade everything on the left of -3
Example #3
Graph x ≥ 6
Draw a shaded circle at 6 and then shade everything on the right of 6
Notice that this time, the circle is shaded because x is also equal to 6.
Example #4
Graph x ≤ -1
Draw a shaded circle at -1 and then shade everything on the left of -1
Example #5
Graph x ≠ 2
x ≠ 2 means that x is equal to any number except 2
Draw a circle at 2 and shade everything on the right and on the left of 2.