"and 10 less than three times that number" -10 + 3n or 3n - 10
"is 8" = 8 n * (3n - 10) = 8 n(3n - 10) = 8
Distribute. [tex]3n^2 - 10n = 8[/tex]
Subtract 8 from both sides. [tex]3n^2 - 10n - 8 = 0[/tex]
Factor. [tex](3n + 2)(n - 4) = 0[/tex]
Set each factor to zero. 3n + 2 = 0 n - 4 = 0
There are two apparent solutions, but we must remember that the problem says that the number is negative. We must therefore discard the second equation as extraneous.
3n + 2 = 0
Subtract 2 from both sides. 3n = -2
Divide both sides by 3. [tex]n = \frac{-2}{3} [/tex]
