I need help solving an equation
Solve the following equation for a. Please show all of your work.
C = 1/6 (10b-7a)
C = 1/6 (10b-7a)
C = (1/6*10b) - (1/6*7a)
C = 5/3 b - 7/6 a
+7/6 a +7/6 a
C + 7/6 a = 5/3 b
-C -C
7/6 a = 5/3 b + C
oops not done.
(7/6 a) / 7/6 = (5/3 b + C)/ 7/6
a = (5/3 b + C)*(6/7)
a = 10/7 b + 6/7 C
multiply both sides by 6
6C = 10b - 7a
7a = 10b - 6C
a = (10/7)b - (6/7)C
To solve for a in the equation C = 1/6 (10b - 7a), we can begin by isolating the variable a.
1. Start by distributing the 1/6 to the terms inside the parentheses:
C = 1/6 * 10b - 1/6 * 7a
C = 10/6b - 7/6a
2. Next, let's move the term containing b to the right side of the equation by subtracting 10/6b from both sides:
C - 10/6b = -7/6a
3. To solve for a, we need to isolate the variable by performing inverse operations. Since a is multiplied by -7/6, we can undo this by dividing both sides by -7/6:
(C - 10/6b) / (-7/6) = (-7/6a) / (-7/6)
4. Simplify the left side of the equation:
(C - 10/6b) * (-6/7) = a
The equation is now solved for a:
a = (-6/7)(C - 10/6b)
To summarize, the solution to the equation C = 1/6 (10b - 7a) is a = (-6/7)(C - 10/6b).