What is Inequalities?
An inequality says that two values are not equal.
a ≠ b says that a is not equal to b
There are other special symbols that show in what way things are not equal.
a < b says that a is less than b
a > b says that a is greater than b
(those two are known as strict inequality)
a ≤ b means that a is less than or equal to b
a ≥ b means that a is greater than or equal to b.
a ≠ b says that a is not equal to b
There are other special symbols that show in what way things are not equal.
a < b says that a is less than b
a > b says that a is greater than b
(those two are known as strict inequality)
a ≤ b means that a is less than or equal to b
a ≥ b means that a is greater than or equal to b.
Sometimes we need to solve like these:
|
Symbol
|
Words
|
Example
|
|---|---|---|
| > |
greater than
|
x + 3 > 2
|
| < |
less than
|
7x < 28
|
| ≥ |
greater than or equal to
|
5 ≥ x - 1
|
| ≤ |
less than or equal to
|
2y + 1 ≤ 7
|
Example
1: 3x
< 7 + 3
Solution: We can simplify 7
+ 3 without affecting the inequality: 3x < 10
Example
2: x
+ 3 < 7
Solution: If we subtract 3 from
both sides, we get:
x + 3 - 3 < 7
- 3 = x < 4
And
that is our solution: x < 4
In
other words, x can be any value less than 4.
Questions:
1) 12 < x + 5? 2) 3y < 15? 3) -2y < -8
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