Sure, let's break down the phrase step by step and represent it as an algebraic expression using the variable [tex]\( x \)[/tex]:
1. Identify the components:
- The phrase says "4 is divided by".
- The difference of "7 and a number".
- Here, "a number" is represented by the letter [tex]\( x \)[/tex].
2. Translate the phrase into mathematical terms:
- "The difference of 7 and a number" means [tex]\( 7 - x \)[/tex]. This is because "difference" indicates subtraction, and the phrase specifies '7' and 'a number' (which we represent as [tex]\( x \)[/tex]).
- "4 is divided by" means we are placing 4 in the numerator of a fraction.
3. Combine these components into an algebraic expression:
- We write the fraction with 4 in the numerator and the difference, [tex]\( 7 - x \)[/tex], in the denominator.
The final algebraic expression that represents the phrase "4 is divided by the difference of 7 and a number" is:
[tex]\[ \frac{4}{7 - x} \][/tex]
