First, expand the term within parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:
15 + 6n = 7(2n + 3)15+6n=7(2n+3)
15 + 6n = (7 xx 2n) + (7 xx 3)15+6n=(7×2n)+(7×3)
15 + 6n = 14n + 2115+6n=14n+21
Next, subtract color(red)(6n)6n and color(blue)(21)21 from each side of the equation to isolate the nn term while keeping the equation balanced:
15 + 6n - color(red)(6n) - color(blue)(21) = 14n + 21 - color(red)(6n) - color(blue)(21)15+6n−6n−21=14n+21−6n−21
15 - color(blue)(21) + 6n - color(red)(6n) = 14n - color(red)(6n) + 21 - color(blue)(21)15−21+6n−6n=14n−6n+21−21
-6 + 0 = 8n + 0−6+0=8n+0
-6 = 8n−6=8n
Now, divide each side of the equation by color(red)(8)8 to solve for nn while keeping the equation balanced:
-6/color(red)(8) = (8n)/color(red)(8)−68=8n8
-6/8 = (color(red)(cancel(color(black)(8)))n)/cancel(color(red)(8))
-(2 xx 3)/(2 xx 4) = n
-(color(red)(cancel(color(black)(2))) xx 3)/(color(red)(cancel(color(black)(2))) xx 4) = n
-3/4 = n
n = -3/4
