Rule 1 : Same quantity (number) can be added to both sides of an equation without changing the equality.
Rule 2 : Same quantity can be subtracted from both sides of an equation without changing the equality.
Rule 3 : Both sides of an equation may be multiplied by the same non-zero number without changing the equality.
Rule 4 : Both sides of an equation may be divided by the same non-zero number without changing the equality.
It should be noted that some complicated equations can be solved by using two or more of these rules together.
SOLVING EQUATIONS HAVING VARIABLE TERMS ON ONE SIDE AND NUMBER(S) ON THE OTHER SIDE
Solve the equation: x/5 +11 = 1/15 and check the result.
\(\frac{x}{5} + 11 = \frac{1}{15}\)=>\( \frac{x}{5}+ 11-11 = \frac{1}{15}-11\)
=>\( \frac{x}{5} = \frac{1}{15}-11\)
=>\( \frac{x}{5} = \frac {1-165}{15}\)
=>\( \frac{x}{5}= \frac {-164}{15}\)
=>\( \frac{x}{5} * 5 = \frac {-164}{15} * 5\)
=>\( x= \frac {-164}{3}\)