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

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durbanville eNotes educator| Certified Educator

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

 

atyourservice | Student

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

multiply the whole thing by 3 to get rid of the fractions

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

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

distribute the 6 into the parenthesis

x-2=9x-6x+6+16
combine like terms

x-2=3x+22

get the like terms on the same side

x-3x=22+2

combine like terms

-2x=24

divide both sides by -2

x=-12

harsha2359 | Student

x/3 - 2/3 = 3x - 2x + 2 + 16/3

2x/3 = -8

x = -12

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