Question

1. write an algebraic expression for the following word phrase: \10 less than the quotient of a number and 3 is 8\

Explanation:

Step1: Define the number

Let the number be \( x \). The quotient of the number and 3 is \( \frac{x}{3} \).

Step2: Apply "10 less than"

"10 less than" the quotient means we subtract 10 from \( \frac{x}{3} \), so the expression is \( \frac{x}{3}- 10 \).

Step3: Set equal to 8

Since this result is 8, the algebraic equation (expression representing the relationship) is \( \frac{x}{3}-10 = 8 \). But if we just need the expression for "10 less than the quotient of a number and 3 is 8", the algebraic expression (equation) is \( \frac{x}{3}-10 = 8 \). If we consider the phrase "10 less than the quotient of a number and 3" first (before relating to 8), it's \( \frac{x}{3}-10 \), and then setting it equal to 8 gives the equation.

Answer:

If we need the equation (since it says "is 8"), the algebraic expression is \( \frac{x}{3}-10 = 8 \) (where \( x \) is the number). If we consider the expression for "10 less than the quotient of a number and 3" (before the "is 8" part), it's \( \frac{x}{3}-10 \). But based on the full phrase "10 less than the quotient of a number and 3 is 8", the algebraic equation is \( \frac{x}{3}-10 = 8 \).