Answer:
r = -7
Step-by-step explanation:
Solve for r:
8 r + 9 = -4 (3 - r) - 7
-4 (3 - r) = 4 r - 12:
8 r + 9 = 4 r - 12 - 7
Grouping like terms, 4 r - 12 - 7 = 4 r + (-7 - 12):
8 r + 9 = 4 r + (-7 - 12)
-7 - 12 = -19:
8 r + 9 = 4 r + -19
Subtract 4 r from both sides:
(8 r - 4 r) + 9 = (4 r - 4 r) - 19
8 r - 4 r = 4 r:
4 r + 9 = (4 r - 4 r) - 19
4 r - 4 r = 0:
4 r + 9 = -19
Subtract 9 from both sides:
4 r + (9 - 9) = -9 - 19
9 - 9 = 0:
4 r = -9 - 19
-9 - 19 = -28:
4 r = -28
Divide both sides of 4 r = -28 by 4:
(4 r)/4 = (-28)/4
4/4 = 1:
r = (-28)/4
The gcd of -28 and 4 is 4, so (-28)/4 = (4 (-7))/(4×1) = 4/4×-7 = -7:
Answer: r = -7
