Answer:
x = 21/20
Explanation:
If you want to find the value of C for which the equation 8x + 3(Cx - 9) = (8x - 8) has a solution x = 21/20, we can plug in x = 21/20 and solve for C:
8(21/20) + 3(C(21/20) - 9) = (8(21/20) - 8)
Let's simplify this equation step by step:
First, simplify the terms on both sides:
(8/20)(21) + 3(C(21/20) - 9) = (8/20)(21) - 8
Simplify the fractions:
(2/5)(21) + 3(C(21/20) - 9) = (2/5)(21) - 8
Simplify further:
42/5 + 3(C(21/20) - 9) = 42/5 - 8
Now, subtract 42/5 from both sides to isolate the term with C:
3(C(21/20) - 9) = 42/5 - 42/5 - 8
Simplify the right side:
3(C(21/20) - 9) = -40/5
Further simplify:
3(C(21/20) - 9) = -8
Divide both sides by 3:
C(21/20) - 9 = -8/3
Add 9 to both sides to isolate C(21/20):
C(21/20) = -8/3 + 9
Simplify the right side:
C(21/20) = (27/3) - (8/3)
C(21/20) = 19/3
Finally, solve for C:
C = (19/3) / (21/20)
To divide fractions, multiply by the reciprocal of the second fraction:
C = (19/3) * (20/21)
Now, multiply the numerators and denominators:
C = (19 * 20) / (3 * 21)
C = 380 / 63
You can simplify this fraction by finding the greatest common divisor (GCD) of 380 and 63, which is 7:
C = (380/7) / (63/7)
C = 54.2857 (rounded to four decimal places)
So, for C ≈ 54.2857, the solution to the equation is x = 21/20.