Question

A) Write an equation in terms of x that represents the problem. (b) Solve the problem.

Seven less than the quotient of a number and 2 is equal to − 12. Find the number.
Part 1 of 2
The equation that represents the problem is _____?
The number is______?

Answer 1

Part 1: (n÷2)-7 = -12

Part 2: n = -10

Explanation:

Part 1:

Let's first write "the quotient of a number and 2" using numbers and variables. Let "n" represent "a number". The key word that we see here is quotient, meaning we have to divide something by something else. "The quotient of a number and 2 means that "a number" is the dividend (number that is divided) and "2" is the divisor (number that divides the dividend). Therefore we obtain:

n÷2

The first part says "seven less than the quotient of a number and 2". The keyword here is less, meaning we have to use subtraction. Therefore:

(n÷2)-7

The last part says "is equal to -12". Therefore the whole expression we just wrote is equivalent to -12:

(n÷2)-7 = -12

Part 2

Remember the Order of Operations:

Parentheses

Exponents

M/D: Multiplication/Division (whichever comes first in the equation)

A/S: Addition/Subtraction (whichever comes first in the equation)

Start by adding 7 to both sides

(n÷2) = -5

Then, multiply both sides by 2

`(n)/(2)=-5\\n=-10`

Note: I used a fraction to display the division because it is easier to see why we have to multiply both sides by 2; to cancel out the denominator.