1. Unit 2 Solve Equations and Systems of Equations
Algebraic Properties to Solve Equations

2. Identity Properties a + 0 = a Identity Property of Addition
If you add 0 to any number, you will get that number.
0 is sometimes called the additive identity.
Identity Property of Multiplication
If you multiply 1 by any number, you will get that number.
1 is sometimes called the multiplicative identity.

3. Inverse Properties Inverse Property of Addition
If you add a number and its opposite, you get 0.
Inverse Property of Multiplication
If you multiply a number by its reciprocal, you get 1.

4. Name the property used in each example.
Inverse Prop. of Addition
= 0
= -3
5(1) = 5
4(¼) = 1
-3•1 = -3
Identity Prop. of Addition
Identity Prop. of Multiplication
Inverse Prop. of Multiplication
Identity Prop. of Multiplication

5. Name the property used in each example.
Identity Prop. of Multiplication
1x = x
-x + x = 0
3x + 0 = 3x
Inverse Prop. of Addition
Inverse Prop. of Multiplication
Identity Prop. of Addition

6. Commutative Properties
Commutative Property of Addition
You can add numbers in any order.
Commutative Property of Multiplication
You can multiply numbers in any order.

7. Associative Properties
Associative Property of Addition
Associative Property of Multiplication

8. Name the property used in each example.
-7 + (-3 + 4) = ( ) + 4 =
5(-2) = -2(5)
(4•3)5 = 4(3•5)
Associative Prop. of Addition
Commutative Prop. of Addition
Commutative Prop. of Multiplication
Associative Prop. Of Multiplication

9. Name the property used in each example.
x(yz) = (xy)z
3x + 5y + -7 = x + 5y
(3 + 5x) + 4 = 3 + (5x + 4)
3(2y) = (2y)3
(-4 + 7) + 3 = 3 + (-4 + 7)
Associative Prop. of Multiplication
Commutative Prop. of Addition
Associative Prop. of Addition
Commutative Prop. of Multiplication
Commutative Prop. of Addition

10. Addition Property of Equality
If a = b, then a + c = b + c.
You can add the same number to both sides of
an equation.
Subtraction Property of Equality
If a = b, then a – c = b – c.
You can subtract the same number from both
sides of an equation.

11. Multiplication Property of Equality
If a = b, then ac = bc.
You can multiply both sides of an equation by the
same number.
Division Property of Equality If a = b, then
You can divide both sides of an equation by any
nonzero number.
Distributive Property a(b + c)
= ab + ac

12. Solve for x. Write the logical steps in the solution to each equation.
1) m + 2 = 10
Subtraction Prop. of Equality
m = 8
2) x - 4 = 6
Addition Prop. of Equality
x = 10

13. Solve for x. Write the logical steps in the solution to each equation.
Division Prop. of Equality
x = 7 4)
(-6)
(-6)
Multiplication Prop. of Equality
-72 = x

14. Solve for x. Write the logical steps in the solution to each equation.
Subtraction Prop. of Equality
2x = 8
Division Prop. of Equality 2 2
x = 4

15. Solve for x. Write the logical steps in the solution to each equation.
Addition Prop. of Equality
(3)
(3)
Multiplication Prop. of Equality
x = 18

16. Solve for x. Write the logical steps in the solution to each equation.
Distributive Prop.
3x - 6 = 17
Addition Prop. of Equality
3x = 23
Division Prop. of Equality

17. Reflexive Property a = a
Any value equals itself.
Symmetric Property If a = b, then b = a.
You can “swap” two sides of an equation.
Substitution Property If a = b, then a can be substituted for b.

18. Solve for x. Write the logical steps in the solution to each equation.
Subtraction Prop. of Equality
(-5)
(-5)
Multiplication Prop. of Equality
-35 = x
x = -35
Symmetric Prop. of Equality

19. Name the property used in each example.
If x = 4, then x + 7 =
If 7 = y, then y = 7.
2 = 2
If x + y = 12, and x = 7, then 7 + y = 12.
Substitution Prop.
Symmetric Prop.
Reflexive Prop.
Substitution Prop.

20. Name the property used in each example.
3 + 2y = 3 + 2y
If 9y = 7, then 7 = 9y.
If a = 3 and b = 7, then ab = (3)(7).
Reflexive Prop.
Symmetric Prop.
Substitution Prop.