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Find the value of c that will make the following two expressions equivalent.

2a+10b-8-2(4a-6) and -6a+20b+c

User Auxdx
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1 Answer

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We can begin by simplifying the first expression:

2a+10b-8-2(4a-6) = 2a+10b-8-8a+12
= -6a+10b+12

Now we need to find the value of c that makes -6a+10b+12 and -6a+20b+c equivalent. In order for them to be equivalent, they must have the same coefficients for a and b. The coefficient for a is already the same (-6), so we just need to make the coefficient for b the same:

10b = 20b
10b - 20b = 0
-10b = 0
b = 0

Now that we have found the value of b, we can substitute it back into either expression to find the value of c:

-6a+10b+12 = -6a+10(0)+12
= -6a+12

-6a+20b+c = -6a+20(0)+c
= -6a+c

Since these expressions are equivalent, their coefficients for a must also be equal:

-6a+12 = -6a+c

Simplifying this equation, we find:

12 = c

Therefore, the value of c that makes the two expressions equivalent is 12.
User Mattias Nordqvist
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