Question

given the expression \\(5x + 7\\), which translation is not a correct match?

• seven more than five times a number
• the sum of five times a number and seven
• five added to seven times a number
• a number multiplied by five, increased by seven

Explanation:

Analyze the given expression

Using the Translating Expressions knowledge point
The given algebraic expression is:

$$ 5x + 7 $$

Here, \(x\) represents "a number". The term \(5x\) represents "five times a number", and adding \(7\) represents "increased by seven", "seven more than", or "the sum of... and seven".

Evaluate the first option

Using the Algebraic Translations knowledge point

• Option: "Seven more than five times a number"
• Translation: "Five times a number" is \(5x\). "Seven more than" means we add \(7\).
• Result: \(5x + 7\)
• This is a correct match.

Evaluate the second option

Using the Algebraic Translations knowledge point

• Option: "The sum of five times a number and seven"
• Translation: "Five times a number" is \(5x\). "The sum of [this] and seven" means we add them together.
• Result: \(5x + 7\)
• This is a correct match.

Evaluate the third option

Using the Algebraic Translations and Translating Expressions knowledge points

• Option: "Five added to seven times a number"
• Translation: "Seven times a number" is \(7x\). "Five added to" means we add \(5\).
• Result: \(7x + 5\)
• This is NOT a correct match for \(5x + 7\).

Evaluate the fourth option

Using the Algebraic Translations knowledge point

• Option: "A number multiplied by five, increased by seven"
• Translation: "A number multiplied by five" is \(5x\). "Increased by seven" means we add \(7\).
• Result: \(5x + 7\)
• This is a correct match.

Answer:

• (A) Seven more than five times a number
• (B) The sum of five times a number and seven
• (C) Five added to seven times a number (Correct answer)
• (D) A number multiplied by five, increased by seven