• To understand the rules for dealing with inequalities.o understand the rules for dealing with inequalities. • To solve linear inequalities.
To solve linear inequalities. • To plot the solutions to inequalities on a number line. To plot the solutions to ineq alities on a number line. qu
The previous chapters examined mathematical statements in which one side is equal to (=) the other side. Inequalities involve mathematical statements where one side is not equal to the other side.
5 > 2 (5 is greater than 2) 2 < 4 (2 is less than 4) x ≤ – 4 (x is less than or equal to – 4) y ≥ 3 ( y is greater than or equal to 3)
8.1 Techniques for handling inequalities
Inequalities are tricky to handle. If you see an inequality, take your time and think about it. To illustrate the techniques for handling inequalities, consider the following numerical example:
WORKED EXAMPLE Start with 8 > 4.
Add +5 to both sides: 13 > 9 [This is a true statement.] Subtract 5 from both sides: 3 > –1 [This is a true statement.] Move all terms to the left: 8 – 4 > 0 [This is a true statement.] Move all terms to the right: 0 > 4 – 8 [This is a true statement.] Switch sides: – 4 > – 8 [This is a true statement.] Multiply both sides by +2: 16 > 8 [This is a true statement.] Divide both sides by +2: 4 > 2 [This is a true statement.]
