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100 pts!

An equation is given, where C is a real number.

8x + 3 (Cx-9)=(8x – 8)
For what value of C is the solution to the equation x = 21/20?

C= ?

100 pts! An equation is given, where C is a real number. 8x + 3 (Cx-9)=(8x – 8) For-example-1
User BSalita
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1 Answer

7 votes

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.

User Halsafar
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