MATH 0960
K. Rigdon
STEPS TO SOLVE Linear Equations
1)
If the equation contains fractions or decimals, multiply both sides of the
equation to clear them (clearing the fractions & decimals is optional, but
recommended)…
 To clear the decimals - Multiply by the largest place value name
(without the “th”)
 to clear the fractions - Multiply by the Least Common Denominator
(LCD)
 REMEMBER: multiply every term, not just the term(s) with the
decimals or fractions, but the whole numbers and/or the terms with
just the variable as well….
 Also remember: whatever is in parentheses in this step is protected
from this multiplication (if further fractions or decimals are inside the
parentheses, you will either need to do step 2 first, or do step 1 a
second time, after you have done step 2)
2)
If the equation contains PARENTHESES, use the DISTRIBUTIVE
PROPERTY to clear them
3)
Combine LIKE TERMS on the SAME SIDE of the equal sign
4)
Use the ADDITION PROPERTY to rewrite the equation so that all the
TERMs with the VARIABLE are ISOLATED on ONE SIDE of the equation
(can also subtract, remember) – may have to use the property twice (once
on term with variable and once on constant term)
 IF THE TERMS WITH THE VARIABLES CANCEL OUT COMPLETELY,
YOU WILL HAVE ONE OF TWO SPECIAL SITUATIONS…
 If the numbers that are left are really equal, then it means
any number you can think of will make the equation true
x = all real numbers (or

)
called IDENTITY
If the numbers that are left are not equal, then it means that
there is no number that will make the equation true
x = the empty set (no solution or
0 )
called
CONTRADICTION
5)
Use the MULTIPLICATION PROPERTY to SOLVE for the variable (can also
divide, remember)
6)
CHECK your solution in the original equation.