Solving a Linear Equation with Faction Coefficients

Example:  Solve the equation.

1 /9 (6t-9)=11/9 t -{t+9}/18

Solution:

Solve the equation by clearing fractions.
1 /9 (6t-9)=11/9 t -{t+9}/18
The least common multiple of the denominators is 18.  Multiply the least common multiple by each term.
1 /9 (6t-9)=11/9 t -{t+9}/18
18*{1 /9} (6t-9)=18*{11/9} t -18*{t+9}/18
As you simplify, the fractions cancel.
18*{1 /9} (6t-9)=18*{11/9} t -18*{t+9}/18
2 (6t-9)=2  (11) t -(t+9)
Use the distributive property and combine like terms.
2 (6t-9)=2  (11) t -(t+9)
12t-18=22 t -t-9
12t-18=21 t -9
Move the variables to one side of the equation and simplify.
12t-18=21 t -9
12t-21t-18=21 t-21t -9
-9t-18=-9
Get the variable by itself on one side of the equation by adding 18 on both sides and dividing by -9.
-9t-18=-9
-9t-18+18=-9+18
-9t=9
{-9t}/-9=9/-9
t=-1