What is the solution to the linear function? 2/3x - 1/2 = 1/3 + 5/6x

  x = -5

Step-by-step explanation:

You are often told to start a problem like this by clearing fractions. Multiply the equation by the least common denominator of the fractions. Here, that value is 6.

  4x -3 = 2 +5x . . . . multiply the equation by 6

  -5 = x . . . . . . . . . . . add -2-4x to both sides

The solution is x = -5.

If you're comfortable with arithmetic using fractions, you can "cut to the chase." Subtract 2/3x+1/3 from both sides:

  (2/3x -1/2) -(2/3x +1/3) = (1/3 +5/6x) -(2/3x +1/3)

  -1/2 -1/3 = 5/6x -2/3x . . . . simplify a little

  -5/6 = 1/6x . . . . . . . . . . . . .simplify more

  -5 = x . . . . . . multiply by 6