First, expand the terms within parenthesis on both sides of the equation:
-2r + 6r - 6 + 3r - 4 + r = -r - 5−2r+6r−6+3r−4+r=−r−5
Next, group and combine like terms on the left side of the equation:
-2r + 6r + 3r + r - 6 - 4 = -r - 5−2r+6r+3r+r−6−4=−r−5
(-2 + 6 + 3 + 1)r - 10 = -r - 5(−2+6+3+1)r−10=−r−5
8r - 10 = -r - 58r−10=−r−5
Then, add color(red)(r)r and color(blue)(10)10 to each side of the equation to isolate the rr terms while keeping the equation balanced:
8r - 10 + color(red)(r) + color(blue)(10) = -r - 5 + color(red)(r) + color(blue)(10)8r−10+r+10=−r−5+r+10
8r + color(red)(r) - 10 + color(blue)(10) = -r + color(red)(r) - 5 + color(blue)(10)8r+r−10+10=−r+r−5+10
9r - 0 = 0 + 59r−0=0+5
9r = 59r=5
Now, divide each side of the equation by color(red)(9)9 to solve for rr while keeping the equation balanced:
(9r)/color(red)(9) = 5/color(red)(9)9r9=59
(color(red)cancel(color(black)(9))r)/cancel(color(red)(9)) = 5/9
r = 5/9
