Question

Five less than the quotient of a number and three is -7

Answer 1

The unknown number is -6

Explanation:

Let's start by writing the sentence in mathematical terms:

Since we don't know what that "number" is, we replace it with the letter "
`x`". Then, the quotient of that unknown number and three can now be written as:
`(x)/(3)`

"Five less than the quotient of a number by three", can then be written as the difference (where we are subtracting 5 from that quotient):
`(x)/(3) -5`

The last part of the sentence tells us that the expression we just wrote in mathematical form "is -7." This in mathematical terms indicates "equals -7."

Therefore, we now have a mathematical equation (there is an equal sign in the expression) and we try to solve for the unknown number "
`x`" in it:

`(x)/(3) -5=7\\`

We do such by isolating the x on one side of the equal sign. This process involves: first add 5 on both sides of the equation, and second:multiply both sides of the equation by 3 to get rid of the denominator under the unknown:

`(x)/(3) -5=-7\\(x)/(3) -5 +5 = -7 +5\\(x)/(3) =-2\\(x)/(3) * 3 = -2 *3\\x=-6`