First, expand the terms within parenthesis on the left side of the equation by multiplying each term within the parenthesis by color(red)(4)4 which is the term outside the parenthesis:
6 + (color(red)(4) xx r) - (color(red)(4) xx 2) = r + 76+(4×r)−(4×2)=r+7
6 + 4r - 8 = r + 76+4r−8=r+7
6 - 8 + 4r = r + 76−8+4r=r+7
-2 + 4r = r + 7−2+4r=r+7
Next, add color(red)(2)2 and subtract color(blue)(r)r from each side of the equation to isolate the rr term while keeping the equation balanced:
-2 + 4r + color(red)(2) - color(blue)(r) = r + 7 + color(red)(2) - color(blue)(r)−2+4r+2−r=r+7+2−r
-2 + color(red)(2) + 4r - color(blue)(r) = r - color(blue)(r) + 7 + color(red)(2)−2+2+4r−r=r−r+7+2
0 + 3r = 0 + 90+3r=0+9
3r = 93r=9
Now, divide each side of the equation by color(red)(3)3 to solve for rr while keeping the equation balanced:
(3r)/color(red)(3) = 9/color(red)(3)3r3=93
(color(red)(cancel(color(black)(3)))r)/cancel(color(red)(3)) = 3
r = 3
