The quotient of a number and -7 , decreased by 2 is 10 . Find the number. le \( n= \) lhe \( \$ \)

Let's break down the problem step by step. 1. **Identify the known conditions:** - We have a number \( n \). - The quotient of this number and -7 is represented as \( \frac{n}{-7} \). - This quotient decreased by 2 equals 10. 2. **Set up the equation:** From the problem statement, we can write the equation as: \[ \frac{n}{-7} - 2 = 10 \] 3. **Solve the equation step by step:** - First, we will isolate the term \( \frac{n}{-7} \) by adding 2 to both sides: \[ \frac{n}{-7} = 10 + 2 \] \[ \frac{n}{-7} = 12 \] - Next, we will multiply both sides by -7 to solve for \( n \): \[ n = 12 \times -7 \] 4. **Calculate the value of \( n \):** Now, let's perform the multiplication: \[ n = -84 \] Thus, the number \( n \) is \( -84 \).