To translate the given statement into an algebraic expression, let's break down the phrase "Eight less than the product of five and a number."
1. Identify the unknown number: Let [tex]\( x \)[/tex] represent the unknown number.
2. Find the product of five and the number: The product of five and the number can be written as [tex]\( 5x \)[/tex].
3. Subtract eight: Eight less than this product means we need to subtract eight from [tex]\( 5x \)[/tex].
Thus, the algebraic expression for "Eight less than the product of five and a number" is [tex]\( 5x - 8 \)[/tex].
Among the given options:
- [tex]\( (5 + x) - 8 \)[/tex] is incorrect because it represents eight less than the sum of five and the number.
- [tex]\( 5x - 8 \)[/tex] is correct.
- [tex]\( 8 - \frac{5}{x} \)[/tex] is incorrect because it represents eight minus the quotient of five and the number.
- [tex]\( 8 - 5x \)[/tex] is incorrect because it represents eight minus the product of five and the number.
Therefore, the correct algebraic expression is [tex]\( 5x - 8 \)[/tex].
