1. Solving Equations by Multiplying or Dividing
Multiplication Property of Equality – you can multiply both sides of an equation by the same #, and the statement will still be true.
Example:
Solve the equation 8x = 32 for x
Step 1: write the equation 8x = 32
Step 2: decide what needs to the 8 needs to move
be moved to the other side
in order to isolate the variable
Step 3: perform the opposite operation 8x/8 = 32/8
to move the constant to the
other side
Step 4: solve/simplify/evaluate x = 4
Step 5: check your work!

2. Division Property of Equality – you can divide both sides of an equation by the same nonzero #, and the statement will still be true.
Example:
Solve the equation n/5 = 7 for n
Step 1: write the equation n/5 = 7
Step 2: decide what needs to the 5 needs to move
be moved to the other side
in order to isolate the variable
Step 3: perform the opposite operation (n/5) (5) = (7) (5)
to move the constant to the
other side
Step 4: solve/simplify/evaluate n = 35
Step 5: check your work!

3. Jack has saved $50, which is one-fourth of the amount he
Example:
Jack has saved $50, which is one-fourth of the amount he
needs for a school trip. What is the total amount he needs?
Step 1: what are they asking for? Total cost of the trip
Step 2: what do we know? $50 saved
that is only ¼ of the total
Step 3: write an equation ¼ times the total cost = $50
¼ t = 50
Step 4: solve for the variable (¼ t )(1/4)= (50) (1/4)
t = 200
Total cost of the trip is $200
Step 5: Now make sure that makes sense!

4. Solving A 2-Step Problem
Sometimes you may have to do 2 inverse operations to solve for a variable.
Example:
Solve 3y – 7 = 20
Step 1: write the problem 3y – 7 = 20
Step 2: move the constant to 3y – =
the other side
Step 3: simplify 3y = 27
Step 4: move the coefficient to (3y) / 3 = (27) / 3
Step 5: simplify/solve y = 9
Step 6: check your work!