Question

9 + 8r = −7 − 4(−r + 3)

Answer 1

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