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 xStep 1: write the equation 8x = 32Step 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 = 4Step 5: check your work!

Solving Equations by Multiplying or Dividing

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!

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!

Solving A 2-Step Problem

Sometimes you may have to do 2 inverse operations to solve for a variable.

Example:Solve 3y – 7 = 20Step 1: write the problem 3y – 7 = 20Step 2: move the constant to 3y – 7 + 7 = 20 + 7

the other sideStep 3: simplify 3y = 27Step 4: move the coefficient to (3y) / 3 = (27) / 3

the other sideStep 5: simplify/solve y = 9Step 6: check your work!