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Lesson 1-4
Solving 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.
Properties of Inequalities
• 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.