Question

Translate the phrases below into inequalities and interval notation. Use the variable x for

the inequalities. The first one is done for you as an example
Phrase Inequality Interval Notation at least 17 x 17 [17,00) at most 17 more than 17 fewer than 17 strictly between 9 and 17 between 9 and 17 inclusive no more than 9

Answer 1

The phrases have been translated into inequalities and interval notation, with inclusive bounds denoted by brackets and exclusive bounds by parentheses. Infinity is used to indicate no upper or lower limits with symbols '(-∞, ...]' or '[..., ∞)'.

Step-by-step explanation:

Translating phrases into inequalities and interval notation involves using mathematical symbols to express the conditions described by the phrases. Here are the translations:

• at least 17 is already given as x ≥ 17 with interval notation as [17, ∞).
• at most 17 translates to x ≤ 17 with interval notation (-∞, 17].
• more than 17 translates to x > 17 with interval notation (17, ∞).
• fewer than 17 translates to x < 17 with interval notation (-∞, 17).
• strictly between 9 and 17 translates to 9 < x < 17 with interval notation (9, 17).
• between 9 and 17 inclusive translates to 9 ≤ x ≤ 17 with interval notation [9, 17].
• no more than 9 translates to x ≤ 9 with interval notation (-∞, 9].

In interval notation, the brackets '[ ]' denote inclusive bounds, while parentheses '( )' denote exclusive bounds. The symbol '∞' represents infinity, indicating that there is no upper or lower limit in that direction.