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Inequalities
- 1. INEQUALITIES Math problems containing <, >, ≤ , and ≥ are called inequalities . For example: 2x+5 < 3x-6
- 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
- 3. INEQUALITIES Solving an inequality means finding all of its solutions
- 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
- 12. INEQUALITIES We will follow these 3 rules to solve linear inequalities
- 13. INEQUALITIES One last thing: ALWAYS EXPRESS THE ANSWER AS AN INTERVAL!
- 14. INEQUALITIES ALWAYS EXPRESS THE ANSWER AS AN INTERVAL! If x>11, the solution is (11, ∞ ) If x ≤ 3, the solution is (- ∞ ,3]