solving equations with variables 1/3x + 2/3 = 5/3x

Question

solving equations with variables 1/3x + 2/3 = 5/3x

Answer 1

when you are solving for equations with variables, you want to combine the like variables and separate them to one side of the equation....

thus, for (1/3)x + (2/3) = (5/3)x, to combine the like variables (x) and separate them to one side of the equation you would subtract (1/3)x from both sides of the equations

    (1/3)x + (2/3) = (5/3)x

   -(1/3)x               -(1/3)x

_________________________

       0    + (2/3) = (5/3)x - (1/3)x

   ===>    (2/3) = (5/3)x - (1/3)x         factor out the x from the right side of the equation

                (2/3) = x ((5/3) - (1/3))    ===>   (2/3) = x ((5-1)/3)   ===>   (2/3) = x (4/3)

   ===>    (2/3) = (4/3)x         multiply both sides of the equation by (3/4) to find x

               (2/3) *= (3/4) * (4/3)x   ===>   (2/4) = x   ===>   x = 1/2

Answer 2

It is important to use parentheses when multiplying/dividing by fractions.  Do you want to solve:

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

or

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

The answer will be different depending on where the parentheses are placed.  In the first equation, the fractions are being multiplied by x, and in the second equation, x is in the denominator of the fraction.

Answer 3

Another way to approach the problem would be to eliminate the fractions altogether by first multiplying the entire equation by least common denominator, which in this case is just 3. Multiplying a fractional equation by the LCD quickly gets rid of all fractions (if done correctly!) and can make the math easier to look at.

3[1/3x + 2/3 = 5/3x].        This gives us
           x + 2 = 5x             Subtract x from both sides to get all variables on one side,
                 2 = 4x             Divide by 4 to get x alone
              1/2 = x             (Since 2/4 = 1/2)