Lesson 1-4 Solving Inequalities

Properties of Inequalities Transitive Property IF a ≤ b and b ≤ c, then a ≤ c. Addition Property If a ≤ b, then a + c ≤ b + c. Subtraction Property If a ≤ b, then a – c ≤ b – c. Multiplication Property If a ≤ b and c > 0, then ac ≤ bc. If a ≤ b and c < 0, then ac ≥ bc. Division Property If a ≤ b and c > 0, then a/c ≤ b/c. If a ≤ b and c < 0, then a/c ≥ b/c.

When you multiply or divide by a negative number you must reverse the inequality symbol. –9x > 18 – ½x < 7

Solving and Graphing Inequalities 3x – 6 < 27 When graphing < or > use an open circle ≥ or ≤ use a closed circle

IF the variable is eliminated there are two possibilities. If the inequality is true, then the solution is all real numbers. If the inequality is false, then there are no solutions.

Solve and graph A) 2x < 2(x + 1) + 3 b) 4(x – 3) + 7 ≥ 4x + 1

A compound inequality is a pair of inequalities joined by and or or. To solve an inequality containing and, find all values of the variable that make both inequalities true. Graph 2x > x + 6 and x – 7 < 2

To solve an inequality containing or, find all values of the variable that make atleast one of the inequalities true. Solve x – 1 < 3 or x + 3 > 8

Assignment: 2 – 34 even on pg 29 – 30.