Question

1. \seven less than the quotient of a number and six is negative ten.\

Explanation:

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the sentence

"The quotient of a number and six" is \( \frac{x}{6} \). "Seven less than" this quotient is \( \frac{x}{6}-7 \). "Is negative ten" gives the equation \( \frac{x}{6}-7 = - 10 \).

Step3: Solve the equation

Add 7 to both sides: \( \frac{x}{6}-7 + 7=-10 + 7 \), which simplifies to \( \frac{x}{6}=-3 \).
Multiply both sides by 6: \( \frac{x}{6}\times6=-3\times6 \), so \( x=-18 \).

Answer:

The number is \( - 18 \)