Solve for r:
2/3-2 r = r/3+7/3
Put each term in 2/3-2 r over the common denominator 3: 2/3-2 r = 2/3-(6 r)/3:
2/3-(6 r)/3 = r/3+7/3
2/3-(6 r)/3 = (2-6 r)/3:
(2-6 r)/3 = r/3+7/3
r/3+7/3 = (r+7)/3:
(2-6 r)/3 = (r+7)/3
Multiply both sides by 3:
2-6 r = r+7
Subtract r from both sides:
2+(-6 r-r) = (r-r)+7
-6 r-r = -7 r:
-7 r+2 = (r-r)+7
r-r = 0:
2-7 r = 7
Subtract 2 from both sides:
(2-2)-7 r = 7-2
2-2 = 0:
-7 r = 7-2
7-2 = 5:
-7 r = 5
Divide both sides of -7 r = 5 by -7:
(-7 r)/(-7) = 5/(-7)
(-7)/(-7) = 1:
r = 5/(-7)
Multiply numerator and denominator of 5/(-7) by -1:
Answer: |r = (-5)/7
