Answer:
a = 1/2
Explanation:
Solve for a:
-7 + 9 a + 5 (7 a - 3) = 0
5 (7 a - 3) = 35 a - 15:
35 a - 15 + 9 a - 7 = 0
Grouping like terms, 35 a + 9 a - 15 - 7 = (9 a + 35 a) + (-7 - 15):
(9 a + 35 a) + (-7 - 15) = 0
9 a + 35 a = 44 a:
44 a + (-7 - 15) = 0
-7 - 15 = -22:
44 a + -22 = 0
Add 22 to both sides:
44 a + (22 - 22) = 22
22 - 22 = 0:
44 a = 22
Divide both sides of 44 a = 22 by 44:
(44 a)/44 = 22/44
44/44 = 1:
a = 22/44
The gcd of 22 and 44 is 22, so 22/44 = (22×1)/(22×2) = 22/22×1/2 = 1/2:
Answer: a = 1/2