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Difficulty: MediumTranslating Word Phrases into Algebraic Equations

Translate the following verbal statement into algebraic expressions representing each side of the equation:

'Eleven less than three times a number, qq, is equal to five times the sum of the number and two.'

Answer:The expression for 'Eleven less than three times a number, qq' is: 【3q - 11】

The expression for 'five times the sum of the number and two' is: 【5(q + 2)】

Answer

The left expression is 3q - 11 and the right expression is 5(q + 2).
The verbal phrase 'less than' requires the subtracted amount to follow the term it modifies, making the first expression 3q - 11. The phrase 'times the sum of' explicitly requires multiplying by a grouped addition, making the second expression 5(q + 2).

Step-by-Step Solution

1
Translate the phrase representing the left side of the equation: 'Eleven less than three times a number, qq'.
3q - 11
The phrase 'three times a number, qq' translates directly to 3q. The phrase 'less than' dictates that 11 is subtracted from 3q, reversing the apparent reading order of the words.
2
Translate the phrase representing the right side of the equation: 'five times the sum of the number and two'.
5(q + 2)
The phrase 'sum of the number and two' translates to (q + 2). Grouping symbols (parentheses) are required because the multiplication by five applies to the entire sum, not just the first term.

Key Concept

Translating complex algebraic phrases by correctly applying order-reversing terminology and grouping indicators.
Estimated Time:1m 0s
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Topics

Translating Word Phrases into Algebraic Equations

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