Which algebraic expression represents the phrase "seven more than half of a number"?
A. [tex]$7-\frac{1}{2} x$[/tex]
B. [tex]$-7+\frac{1}{2} x$[/tex]
C. [tex]$\frac{1}{2} x+7$[/tex]
D. [tex]$-\frac{1}{2} x-7$[/tex]
Answer (2)
The algebraic expression that represents "seven more than half of a number" is 2 1 x + 7 . The correct option from the choices provided is C. This interpretation is achieved by expressing half of the number as 2 1 x and adding 7.
;
Represent the unknown number with a variable: x .
Express "half of the number" as 2 1 x .
Add 7 to represent "seven more than": 2 1 x + 7 .
The algebraic expression is 2 1 x + 7 .
Explanation
Understanding the Phrase Let's break down the phrase "seven more than half of a number" to translate it into an algebraic expression.
Representing the Unknown Number First, we identify the unknown number. We can represent this number with a variable, let's use x .
Finding Half of the Number Next, we need to find "half of the number". This can be written as 2 1 x .
Adding Seven Finally, we need to add "seven more than" to half of the number. This means we add 7 to the expression 2 1 x . So, the expression becomes 2 1 x + 7 .
Final Answer Therefore, the algebraic expression that represents the phrase "seven more than half of a number" is 2 1 x + 7 .
Examples
Imagine you're baking cookies and a recipe calls for 'seven more than half the amount of sugar' you usually use. If you normally use x cups of sugar, this expression, 2 1 x + 7 , tells you exactly how much sugar to add for this new recipe. This kind of translation from words to algebra is super useful in everyday situations where you need to calculate quantities based on descriptions!
