1. Writing and Graphing Inequalities
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How can you call a mathematical statement that compares two quantities which are not necessarily equal?
Inequality.
We are asked to complete the following sentence.
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A mathematical sentence using the symbols <, >, ≤, or ≥ is called a(n) ?. |
| Symbol | Meaning |
|---|---|
| < | is less than |
| > | is greater than |
| ≤ | is less than or equal to |
| ≥ | is greater than or equal to |
Notice that all these symbols are used to compare two quantities. They express a situation when the quantities are not necessarily equal (≤ and ≥) or when they are never equal (< and > ). We call this type of sentence an inequality. Let's look at some examples!
| Real-Life Situation | Inequality |
|---|---|
| The temperature t of the ocean when not frozen is above -2 ^(∘) C. | t > - 2 |
| If there are fewer than 10 people p, they get no discount in the museum. | p < 10 |
| The temperature t of the ocean when it is frozen is no more than -2 ^(∘) C. | t ≤ - 2 |
| To get a group discount in the museum, there must be at least 10 people p. | p ≥ 10 |
We can see that we are using the given symbols when writing inequalities. Therefore, we can finally complete the given sentence.
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A mathematical sentence using the symbols <, >, ≤, or ≥ is called a(n) inequality. |