Solving Equations
Solving Equations with Addition and Subtraction
You can add or subtract the same number on each side of an
equation and the result is an equivalent equation
. Equivalent equations have the same solution.
Addition Property of Equality 
For any numbers a, b, and c, if a = b,
then a + c = b + c. 
Subtraction Property of Equality 
For any numbers a, b, and c, if a = b,
then a  c = b  c. 
Solving Equations 
To solve an equation
means to get the variable (with a coefficient of 1) by
itself on one side of the equation. You can do this by
undoing what has been done to the variable, using the
properties of equality. 
Example
Solve .
Solution
The number has been subtracted from x. The opposite
of subtracting is adding .
Add to each side of the equation.
is an equivalent equation. Simplify to obtain x = 1.
Check: Is ? Yes. The solution is 1.
Solving Equations with Multiplication and Division
You can solve a multiplication or division equation by using
the multiplication and division properties of equality.
Multiplication Property of
Equality 
For any numbers a, b, and c, if a = b,
then ac = bc. 
Division Property of Equality 
For any numbers a, b, and c, with c 0, if a = b, then . 
Example
Solve
Solution
Rewrite the mixed numbers as improper fractions.
Multiply each side by ,
the reciprocal of the number that is multiplied by x.
Solving MultiStep Equations
Solving MultiStep Equations 
 Work backward to isolate the variable and solve
the equation.
 Use subtraction to undo addition, and use
addition to undo subtraction.
 Use multiplication to undo division, and use
division to undo multiplication.

Consecutive integers are integers in counting
order, such as 3, 2, and 1.
Example
Solve .
Solution
Multiply each side by 4 to eliminate the fraction.
Next, undo the subtraction by adding 3 to each side.
2x  3 + 3 = 36 + 3
2x = 39
Last, undo the multiplication by dividing each side by 2.
