For what value of x do the expressions 2/3x+2 and 4/3x+6 have the same value?

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  x = -6

Step-by-step explanation:

To find the desired value of x, set the expressions equal.

  2/3x +2 = 4/3x +6

Subtract 2/3x +6 from both sides.

  -4 = 2/3x

Multiply by the inverse of the coefficient of x.

  (3/2)(-4) = x = -6

The value of x that makes the expressions have the same value is -6.

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Check

  2/3x +2 = 2/3(-6) +2 = -4 +2 = -2

  4/3x +6 = (4/3)(-6) +6 = -8 +6 = -2 . . . . same value