Which phrase represents the algebraic expression $5 x-9$?
A. the product of five times a number and nine
B. the difference of nine times a number and five
C. the sum of five times a number and five
D. the difference of five times a number and nine
Answer (2)
The algebraic expression 5 x − 9 can be described as 'the difference of five times a number and nine'. Therefore, the correct answer is option D. This accurately encapsulates what the expression represents mathematically.
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The expression 5 x represents 'five times a number'.
The term − 9 represents 'the difference of ... and nine'.
Combining these, the expression 5 x − 9 is 'the difference of five times a number and nine'.
The correct phrase is the difference of five times a number and nine .
Explanation
Analyzing the Expression We need to identify the phrase that correctly describes the algebraic expression 5 x − 9 . Let's break down the expression:
5 x means '5 multiplied by x ', which can be read as 'five times a number'. − 9 means we are subtracting 9, which can be read as 'the difference of ... and nine'.
Combining these, we look for the phrase that means 'the difference of five times a number and nine'.
Evaluating the Options Now, let's examine the given options:
'the product of five times a number and nine' - This would be 5 x × 9 or 5 x 9 , which is not our expression.
'the difference of nine times a number and five' - This would be 9 x − 5 , which is not our expression.
'the sum of five times a number and five' - This would be 5 x + 5 , which is not our expression.
'the difference of five times a number and nine' - This matches our expression 5 x − 9 .
Identifying the Correct Phrase Therefore, the correct phrase is 'the difference of five times a number and nine'.
Examples
Algebraic expressions are used in everyday life to represent various situations. For example, if you earn $5 per hour and need to subtract $9 for transportation costs, the expression 5 x − 9 represents your net earnings after working x hours. Understanding how to translate algebraic expressions into phrases helps in interpreting and solving real-world problems.
