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: [tex]4 (n-7)[/tex]
So we have the expression is:
[tex]4 (n-7) = 12[/tex]
We apply distributive property to the terms within parentheses:
[tex]4n-28 = 12[/tex]
We add 28 to both sides:
[tex]4n = 12 + 28\\4n = 40[/tex]
We divide between 4 on both sides:
[tex]n = \frac {40} {4}\\n = 10[/tex]
Answer:
[tex]n=10[/tex]
