Solve. A) 1/3(x-2)=3x-2(x-1)+16/3

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Solve: `1/3(x-2) = 3x-2 (x-1) + 16/3`

Eliminate the denominator in order to simplify the equation:

`3 times (1/3(x-2)) = 3 times 3x - 3 times 2(x-1) + 3 times 16/3`

Notice how the denominators cross cancel with the fractions:

`(x-2) = 9x - 6(x-1) + 16`

Simplify:

x-2= 9x - 6x + 6 +16

Note how the symbol changed when two negatives were multiplied (-6 x -1)

Now get your x-es together and solve:

x - 9x +6x = 6 +16 + 2

-2x= 24

`therefore x= 24/(-2)`

`therefore` x= - 12

 

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