Using the Language of Algebra
Inequality
$$ \text{a < b is read "a is less than b" a is to the left of b on the number line} $$
$$ \text{a > b is read "a is greater than b" a is to the right of b on the number line}$$
The expressions \(a < b\) or \(a > b\) can be read from left to right or right to left, though in English we usually read from left to right (Table 1.3). In general, \(a < b\) is equivalent to \(b > a\). For example \(7 < 11\) is equivalent to \(11 > 7\). And \(a > b\) is equivalent to \(b < a\). For example \(17 > 4\) is equivalent to \(4 < 17\).
| Inequality Symbols | Words |
|---|---|
| \(a≠b\) | \(\text{a is not equal to b}\) |
| \(a < b\) | \(\text{a is less than b}\) |
| \(a≤b\) | \(\text{a is less than or equal to b}\) |
| \(a > b\) | \(\text{a is greater than b}\) |
| \(a≥b\) | \(\text{a is greater than or equal to b}\) |
Example 1.12
Translate from algebra into English:
-
$$17≤26$$
-
$$8≠17−3$$
-
$$12>27÷3$$
- $$y+7<19$$
Solution
- $$17≤26$$
17 is less than or equal to 26
- $$8≠17−3$$
8 is not equal to 17 minus 3
- $$12>27÷3$$
12 is greater than 27 divided by 3
- $$y+7<19$$
y plus 7 is less than 19
Source: OpenStax, https://openstax.org/books/elementary-algebra/pages/1-2-use-the-language-of-algebra
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