Inequality

\( \text{a < b is read "a is less than b" a is to the left of b on the number line} \)

a < b

\( \text{a > b is read "a is greater than b" a is to the right of b on the number line}\)

a > b

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:

  1. \(17≤26\)

  2. \(8≠17−3\)

  3. \(12>27÷3\)

  4. \(y+7<19\)
Solution
  1. \(17≤26\)

    17 is less than or equal to 26

  2. \(8≠17−3\)

    8 is not equal to 17 minus 3

  3. \(12>27÷3\)

    12 is greater than 27 divided by 3

  4. \(y+7<19\)
    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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