Post on 23-Feb-2016
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INEQUALITY STATEMENTS
• “<“ looks like an alligator’s open mouth. The wider part of the opening points toward the larger number.
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toequalorthangreateristoequalorthanlessis
thangreateristhanlessis
Example……1. 8>2
2. X<3
You cannot list them all because they are infinite but you can show them on a graph.
1. 8 is greater than 2
2. The set of all numbers that make x less than 3
Example……• X<3 would be graphed like this:
• “OPEN Circle” – means the number is NOT part of the solution.
• “CLOSED Circle” = means the number IS part of the solution.
Order of the inequalities……• 8>-4 means the same as -4<8.
• Keep the big mouth pointing toward the same number on either side.
Example…... x 3
Graph: x>2
Graph: x ≤2
Graph: x ≥−3
Graph: x<−5
So what if I took an inequality such as 4 < 8 and added 3 to each side….
So what if I took an inequality such as 4 < 8 and added -5 to each side….
Addition Property of Inequalities• If the same number is added to each side of a true inequality, the resulting inequality is also true.
• 1. If a > b, then a + c > b + c• 2. If a < b, then a + c < b + c
Solve: 𝑥−3>8
Solve: 45≤𝑚−5
Solve: 𝑥+12≤20
Set-Builder Notation• {x | x > 3}
Solve: 27+𝑚>23
Solve: 8−𝑝≤12
Solve: 8 𝑎+4≥7𝑎
Phrases for Inequalities• (<) Less than or fewer than
• (>) Greater than or More than
• ( at most, no more than, less than or equal to
• () at least, no less than, greater than or equal to
Jill has $85 to spend. She went to the store and bought a shirt for $35 and a belt for $18. If she wants to buy a necklace , how much can she spend?
Twice a number increased by 4 is at least 10 more than the number.
Homework• Worksheet