1-5 Solving Inequalities

1. 1-5 Solving Inequalities Solve and graph inequalities by using properties of inequalities.

2. Graphing Inequalities • Open dot for < or > • Closed dot for ≥ or ≤ • If the inequality symbol is open toward the variable, shade to the right. • If the inequality symbol is pointed toward the variable, shade to the left.

3. Properties of Inequalities • If you multiply or divide both sides of an inequality by a negative number, the symbol flips.

4. Solving • Use inverse operations • Graph the solution

5. No Solution or All Real Numbers • There is no solution if all variables cancel and the statement is false. • Ex: -2 > 7 (no variables and we know that -2 is not greater than 7) • All real numbers are solutions if all variables cancel and the statement is true. • Ex: -15 ≤ 8 (no variables and it is true that -15 is less than 8) • Same as infinitely many solutions

6. Compound Inequality Consists of two distinct inequalities joined by the word and or the word or

7. Using the word “And” • Contains the overlap of the graphs of two inequalities that form a compound inequality. • EX: x ≥ 3 and x ≤ 7 • Can also be written 3 ≤ x ≤ 7 • This is only for a compound inequality using the word “and”

8. Using the word “Or” Contains each graph of the two inequalities that form the compound inequality. Used when there is no overlap. EX: x < -2 or x ≥ 1

9. Solving A solution to a compound inequality involving and is any number that makes both inequalities true. EX: -3 ≤ m – 4 < -1 Isolate the variable by adding 4 to each piece -3 + 4 ≤ m – 4 + 4 < -1 + 4 1 ≤ m < 3

10. Solving A solution to a compound inequality involving or is any number that makes either inequality true. You must solve each inequality separately. EX: 3t + 2 < -7 or -4t + 5 < 1 3t < -9 or -4t < -4 t < -3 or t > 1

11. Assignment • Odds p.38 #27-31, 39-43