Addition Property of Equality
Some Examples
Example 1:
Add opps:
Complete the step:
Then
Check: 


Note: (5 â€“ 2) = 3
the coefficient of x is 1.
[Replace x with 3 to check.] 
Example 2:
Add opps:
Complete the step:
Then
Check: 


Note:
the coefficient of x is 1.
[Replace x with
to check.]

Solve Equation with Balance Beam
Pattern: a x + b = c x + d
Both sides are siimplliiffiied and 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:
Then: 

Let A = (c â€“ a) and B = (b â€“ d)
A = 1 is coefficient of x 
Example 1:
Add opps:Complete step:
Then:
Thus: 

Note that 3 > 2
Add same to both sides
(3 â€“ 2) = 1 and (5 + 4) = 9 
Check:
or 

Note 3 Â· 9 = 27
x = 9 is correct 
Some problems have parentheses that have to be removed and terms rearranged before
working with the balance beam. Use the distributive property and associative
property to simplify before solving.
Example 2:
Add opps:Complete step:
Then:
Thus: 
4(2x + 1) = 7(x â€“ 1) + (2 â€“ 6)
8x + 4 = (7x â€“ 7) â€“ 4
8x + 4 = 7x + (â€“ 7 â€“ 4)

Distributive PropertyAssociative Property
Note that 8 > 7
Add same to both sides
(8 â€“ 7) = 1 and (11 â€“ 4) = 15

Check:
4[2(15) + 1] = 7[(15) â€“ 1] + (2 â€“ 6)
4[30 + 1] = 7(16) â€“ 4
4(29) = 112 â€“ 4
or 116 = 116
x = 15 is correct
Remember â€“ always check your answers in the original equation.
