Multiplication Property of Equality
Examples
Example 1:
Solve

Multiply recip: 

Distributive Property 

Associative Property 

Recall

Example 2:

Multiply recip: 

Distributive Property 

Associative Property 

Note

Check:

Replace x with
to check. 
Solve Equation with a Balance Beam
Pattern: ax + b = cx + d
Both sides siimplliiffiied (a ,b, c, d are integers.)
Look at the coefficients of x and determine which is the larger integer (furthest
to the right on the number line). If c > a then we will keep the variiablle x on
tthatt siide of the equation and keep the constant on the other side. To
do this we first add opposites on the balance beam below the equation.
Look at the pattern, and then follow the same steps through several examples
Solve simplified equations vertically  using the balance beam.
Pattern: c > a
1) Add opps:
Complete the step: (b  d) = (c  a)x →
Let A = (c  a) and B = (b  d)
Then: B = A x → A > 1 is coefficient of x
2) Multiply recip:
→ Since
Example 3:
Solve
1) Add opps:


Note that 6 > 2 (Add same to both sides) 
Complete the step: 
(6  2)x = (5 + 3) 
Now (6  2) = 4 and (5 + 3) = 8 4 is the coefficient of
x 
2) Multiply recip:
Then 
x = 2 
Since

3) Check: 

Note that 6 Â· 2 = 12
x = 2 is correct. 
