inequality statements

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