Question

12 less than the quotient of a number and seven is -2 find the number

Answer 1

Let’s break everything down to find the equation first. Let’s have the mysterious number known as N.
12 less than the quotient of a number and seven.
So, we know that N will be divided by seven, as it says “quotient of a number and seven”. The quotient is the answer after a division sentence.
(N/7)
After dividing, we have to subtract 12 from it. It says “less than”, signifying we will have to take away.
N/7-12
Is -2
So the equation is:
N/7-12=-2
Let’s solve.
We need to add 12 to each side of the equation so that hopefully we will get N by itself.
N/7=10
We now need to multiply each side by 7, so N is by itself.
N=70
So the number’s value is 70.

Answer 2

A quotient is the result of a division.
Let the unknown number be x.

We translate the problem into an equation, piece by piece.

"quotient of a number and seven"  ---->   x/7

"12 less than the quotient of a number and seven"  ---->    x/7 - 12

The word "is" means "="
x/7 - 12 =

All the above is -2, so it equals -2.

x/7 - 12 = -2

$\dfrac{x}{7} - 12 = -2$

First, add 12 to both sides and simplify.

$\dfrac{x}{7} - 12 + 12 = -2 + 12$


$\dfrac{x}{7} = 10$

Next, multiply both sides by 7.

$\dfrac{x}{7} \times 7 = 10 \times 7$

$x = 70$

Answer: The number is 70.