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Zorluk: ZorTranslating Word Phrases into Algebraic Equations

Match each complex verbal phrase with its correct algebraic expression representation.

  • Twice the difference when seven is subtracted from three times a number xx2(3x−7)2(3x - 7)
  • Three times a number xx subtracted from the square of five more than the number(x+5)2−3x(x + 5)^2 - 3x
  • The quotient of five less than twice a number xx and three more than the number2x−5x+3\frac{2x - 5}{x + 3}
  • The sum of a number xx and four, divided by the product of three and the number, all decreased by eightx+43x−8\frac{x + 4}{3x} - 8

Cevap

The correct pairings match each complex verbal description with its respective mathematical translation: 'Twice the difference...' pairs with 2(3x−7)2(3x - 7); 'Three times a number...' pairs with (x+5)2−3x(x + 5)^2 - 3x; 'The quotient of...' pairs with 2x−5x+3\frac{2x - 5}{x + 3}; and 'The sum of...' pairs with x+43x−8\frac{x + 4}{3x} - 8.
Each verbal phrase contains specific operational keywords ('quotient', 'product', 'sum', 'difference') and ordering phrases ('subtracted from', 'less than'). Correct translation requires accurately identifying the operations, maintaining the proper sequence, and utilizing grouping symbols where compound expressions are modified.

Adım Adım Çözüm

1
Analyze the first phrase: 'Twice the difference when seven is subtracted from three times a number xx'.
The phrase translates to 2(3x−7)2(3x - 7).
The phrase 'subtracted from' reverses the order, making it 3x−73x - 7. 'Twice the difference' requires multiplying the entire grouping by 2.
2
Analyze the second phrase: 'Three times a number xx subtracted from the square of five more than the number'.
The phrase translates to (x+5)2−3x(x + 5)^2 - 3x.
The base quantity is 'five more than the number' (x+5x + 5), which is then squared to become (x+5)2(x + 5)^2. Subtracting 3x3x from this quantity gives the final expression.
3
Analyze the third phrase: 'The quotient of five less than twice a number xx and three more than the number'.
The phrase translates to 2x−5x+3\frac{2x - 5}{x + 3}.
'Quotient' implies a division. The first part, 'five less than twice a number', forms the numerator (2x−52x - 5). The second part, 'three more than the number', forms the denominator (x+3x + 3).
4
Analyze the fourth phrase: 'The sum of a number xx and four, divided by the product of three and the number, all decreased by eight'.
The phrase translates to x+43x−8\frac{x + 4}{3x} - 8.
The fraction is constructed with 'the sum' (x+4x + 4) over 'the product' (3x3x). The phrase 'all decreased by eight' instructs to subtract 8 from the complete fraction.

Anahtar Kavram

Accurately identifying operational keywords and recognizing the correct order of translation for phrases like 'less than' and 'subtracted from'.
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Konular

Translating Word Phrases into Algebraic Equations

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