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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