Question

Right and solve an equation to find the number n.four times a difference of a number and seven is 12

Answer 1

The equation representing the statement is 4(n - 7) = 12, and by applying algebraic techniques the solution for the number n is found to be 10.

Step-by-step explanation:

The equation that represents the statement 'four times a difference of a number and seven is 12' can be written as 4(n - 7) = 12. To solve for n, we start by distributing the 4 into the parentheses to get 4n - 28 = 12. Next, we add 28 to both sides of the equation to get 4n = 12 + 28, which simplifies to 4n = 40. Finally, we divide both sides by 4 to isolate n, giving us n = 40 / 4, or n = 10. Therefore, the number n is 10.

Answer 2

For this case we must propose an algebraic expression associated with:

"four times a difference of a number and seven is 12"

So we have to:

Four times a difference of a number and seven is represented as:
`4 (n-7)`

So we have the expression is:

`4 (n-7) = 12`

We apply distributive property to the terms within parentheses:

`4n-28 = 12`

We add 28 to both sides:

`4n = 12 + 28\\4n = 40`

We divide between 4 on both sides:

`n = \frac {40} {4}\\n = 10`

Answer:

`n=10`