Sure! Let's break down the phrase "The quotient of 7 and the difference of a number and 8" and convert it into an algebraic expression.
1. Identify "a number": Let's represent "a number" using the variable [tex]\( x \)[/tex].
2. Identify the "difference of a number and 8": This translates to [tex]\( x - 8 \)[/tex].
3. Forming the quotient: "The quotient of 7 and the difference of a number and 8" means we need to divide 7 by the expression [tex]\( x - 8 \)[/tex].
Putting it all together, the algebraic expression is:
[tex]\[
\frac{7}{x - 8}
\][/tex]
So, the expression representing the given phrase is [tex]\( \frac{7}{x - 8} \)[/tex].
