Answer:
a = -4 or 3a+12=0 (not sure what you want)
Explanation:
Solve for a:
8 a - (15 - a) = 6 (a - 7) + 15
-(15 - a) = a - 15:
8 a + a - 15 = 6 (a - 7) + 15
Grouping like terms, 8 a + a - 15 = (8 a + a) - 15:
(8 a + a) - 15 = 6 (a - 7) + 15
8 a + a = 9 a:
9 a - 15 = 6 (a - 7) + 15
6 (a - 7) = 6 a - 42:
9 a - 15 = 6 a - 42 + 15
Grouping like terms, 6 a - 42 + 15 = 6 a + (15 - 42):
9 a - 15 = 6 a + (15 - 42)
15 - 42 = -27:
9 a - 15 = 6 a + -27
Subtract 6 a from both sides:
(9 a - 6 a) - 15 = (6 a - 6 a) - 27
9 a - 6 a = 3 a:
3 a - 15 = (6 a - 6 a) - 27
6 a - 6 a = 0:
3 a - 15 = -27
Add 15 to both sides:
3 a + (15 - 15) = 15 - 27
15 - 15 = 0:
3 a = 15 - 27
15 - 27 = -12:
3 a = -12
Divide both sides of 3 a = -12 by 3:
(3 a)/3 = (-12)/3
3/3 = 1:
a = (-12)/3
The gcd of -12 and 3 is 3, so (-12)/3 = (3 (-4))/(3×1) = 3/3×-4 = -4:
Answer: |
| a = -4Solve for a:
8 a - (15 - a) = 6 (a - 7) + 15
-(15 - a) = a - 15:
8 a + a - 15 = 6 (a - 7) + 15
Grouping like terms, 8 a + a - 15 = (8 a + a) - 15:
(8 a + a) - 15 = 6 (a - 7) + 15
8 a + a = 9 a:
9 a - 15 = 6 (a - 7) + 15
6 (a - 7) = 6 a - 42:
9 a - 15 = 6 a - 42 + 15
Grouping like terms, 6 a - 42 + 15 = 6 a + (15 - 42):
9 a - 15 = 6 a + (15 - 42)
15 - 42 = -27:
9 a - 15 = 6 a + -27
Subtract 6 a from both sides:
(9 a - 6 a) - 15 = (6 a - 6 a) - 27
9 a - 6 a = 3 a:
3 a - 15 = (6 a - 6 a) - 27
6 a - 6 a = 0:
3 a - 15 = -27
Add 15 to both sides:
3 a + (15 - 15) = 15 - 27
15 - 15 = 0:
3 a = 15 - 27
15 - 27 = -12:
3 a = -12
Divide both sides of 3 a = -12 by 3:
(3 a)/3 = (-12)/3
3/3 = 1:
a = (-12)/3
The gcd of -12 and 3 is 3, so (-12)/3 = (3 (-4))/(3×1) = 3/3×-4 = -4:
Answer: a = -4