Math 010 - Cooley
Elementary Algebra
OCC
Section 2.2 – Using the Principles Together
 Example:
Solve: 7 x  5  16 .
Solution:
7 x  5  16 .
7 x  5  (5)  16  (5)
7 x  21
7 x  21

7
7
x  3
Using the addition principle, subtract 5 from both sides (adding –5).
Simplify.
Using the multiplication principle, divide both sides by 3 (multiplying by
1
3
).
Simplify. Don’t forget to check your solution. (Not shown).
Equation-Solving Procedure
1. Use the multiplication principle to clear any fractions or decimals. (Optional)
2. If necessary, use the distributive law to remove parentheses. Then combine like terms on each side.
3. Use the addition principle, as needed, to isolate all variable terms on one side. Then combine like terms.
4. Multiply or divide to solve for the variable, using the multiplication principle.
5. Check all possible solutions in the original equation.
 Exercises:
Solve and check
1)
5 x  9  41
2)
 39  1  8 x
3)
12  4 x  108
4)
6
5)
6x  5  7  2x
6)
5(2t  2)  30
5
x  4
4
-1-
Math 010 - Cooley
Elementary Algebra
OCC
Section 2.2 – Using the Principles Together
 Exercises:
Solve and check
7)
6b  (3b  8)  16
8)
2 y  15  5 y  3
9)
5(t  3)  9  3(t  2)  6
10)
12(2  c)  15  8  3(4c  9)
11)
3
x  2  3x  9
8
12)
7
1 3
1
x  x x
8
4 4
16
13)
4
5x  1  8
3
14)
3
2 x  5   15
2
2
-2-