In the first side of the equation: 1 + 3n + 7n You can see that there's the addition of the same variable but with different coefficients. Their addition gives the same variable with the addition of the coefficients: 1 + 3n + 7n = 1 + (3+7)n = 1 + 10n
In the second side of the equation: 7(n+4) + 6(3n + 3) Let's develop both parts of equation: 7(n+4) = 7n + 28 6(3n + 3) = 18n + 18 So 7(n+4) + 6(3n + 3) = 7n + 28 + 18n + 18 Same thing as the first side, you add the variables between each others and the numbers between each others: 7n + 18n + 28 + 18 = 25n + 46
So we can now retype the equation: 1 + 3n + 7n = 7(n+4) + 6(3n+3) 1 + 10n = 25n + 46 Now to solve for n, you need to have the variables on a side and the numbers on the other. So first subtract 25n from each side: 1 + 10n - 25n = 25n - 25n + 46 1 + 10n - 25n = 46 Then subtract 1 from each side: 1 + 10n - 25n -1 = 46 - 1 10n - 25n = 46 - 1 Now simple calculus: - 15n = 45 Now divide each side by -15 to get the variable n alone on a side and its value on the other side: (-15n)/-15 = 45/-15 n = -3
You can recheck your answer (very important): 1 + 3n + 7n = 1 + 3(-3) + 7(-3) = 1 - 9 - 21 = -29 7(n+4) + 6(3n + 3) = 7(-3+4) + 6(3*-3 + 3) = 7 + 6*-6 = 7 - 36 = -29 So 1 + 3n + 7n = 7(n+4)+6(3n+3) = -29 The answer has been approved.