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1.5 Solving Inequalities I. Solving and Graphing Inequalities As with equations, the solutions of an inequality are numbers that make it true. A. Properties of Inequalities Most important inequality properties are the ones of Multiplication and Division. When multiplying or dividing both sides by a negative number, the negative operation reverses the direction of the inequality symbol. Example 1: 6 + 5(2 – x) ≤ 41 Hint: ≤ & ≥ are shaded when graphing the inequality Example 2: 3x – 12 < 3 Hint: < & > are open when graphing the inequality B. No Solutions or All real # Solutions All real #’s are Solutions! Example 3: 2x – 3 > 2(x – 5) Example 4: 7x + 6 < 7(x – 4) II. Compound Inequalities Compound Inequalities is a pair of inequalities joined by and or or. A. To solve compound inequalities containing and find all values of the variable that make both inequalities true. Example 1: Solve and Graph 3x-1 > -28 and 2x + 7 < 19 B. To solve a compound inequality containing or, find all values of the variable that make at least one of the inequalities true. Example 2: Solve and Graph 4y – 2 ≥ 14 or 3y – 4 ≤ -13