2. INEQUALITIES A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement. For example: 50 is a solution of 2x+5 < 3x-6 because 2·50+5<3·50-6
4. INEQUALITIES When solving inequalities, there are certain manipulations of the inequality which do not change the solutions. In other words, there are rules you have to follow to solve an inequality
5. INEQUALITIES When solving inequalities, there are certain manipulations of the inequality which do not change the solutions. In other words, there are rules you have to follow to solve an inequality.
6. INEQUALITIES Rule 1 You may add or subtract any number to both sides of an inequality.
7. INEQUALITIES Rule 1 You may add or subtract any number to both sides of an inequality. Example : In 2x+5 < 3x-6, we can subtract 5 to both sides: 2x<3x-6-5 And then subtract 3x to both sides: -x<-11
8. INEQUALITIES Rule 2 You may multiply or divide both sides of an inequality by any positive number.
9. INEQUALITIES Rule 2 You may multiply or divide both sides of an inequality by any positive number. Example : In 3x<18, we can divide both sides by 3: x<6
10. INEQUALITIES Rule 3 If you multiply or divide both sides of an inequality by a negative number, reverse the direction of the inequality sign
11. INEQUALITIES Rule 3 If you multiply or divide both sides of an inequality by a negative number, reverse the direction of the inequality sign Example : In the previous example, -x<-11, we can multiply both sides by -1: x>11