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Agenda
1. Warm Up
2. Algebraic Properties Notes
3. Solving Multi-Step Equations Notes
4. Solving Multi-Step Equations CW
NOTEBOOK EXAMPLE
Ex.1
Ex.2
Ex.3
Ex.4
Ex.5
ALGEBRAIC PROPERTIES
Properties of Equality
Addition Property of Equality
If a = b, then a + c = b + c.
Subtraction Property of Equality
If a = b, then a – c = b – c.
Multiplication Property of Equality
If a = b, then ac = bc.
Division Property of Equality
If a = b, then a/c = b/c.
ALGEBRAIC PROPERTIES
Substitution Property of Equality
If a = b then a can be substituted for b,
and vice versa
Symmetric Property of Equality
If a = b, then b = a.
Distributive Property of Multiplication
a(b + c) = ab + ac
** On a step where you combine like terms, the justification is “Simplify” **
EX. OF PROOF USING PROPERTIES
EX. OF 2 COLUMN PROOF USING PROPERTIES
EX.1 SOLVE FOR B AND JUSTIFY EACH STEP
-b + 9 = 10b
EX.2 SOLVE FOR X AND JUSTIFY EACH STEP
5x – 3 = 2x + 12
EX.3 SOLVE FOR H AND JUSTIFY EACH STEP
$60 + $1.50h = $5.50h
EX.4 SOLVE FOR Y AND JUSTIFY EACH STEP
5(y - 3) = 19
EX.5 SOLVE FOR A AND JUSTIFY EACH STEP
𝑎 5 6
− =
7 7 7
EX.6 SOLVE FOR M AND JUSTIFY EACH STEP
𝑚
2
−7=
6
3
PRACTICE: SOLVE FOR X AND JUSTIFY EACH STEP
2
5
𝑥− 𝑥=2
3
8
EX.7 SOLVE FOR Y
4 - 4y = -4y + 4
This is called Identity, it is
exactly the same on both
sides. There are an infinite #
of solutions. In fact, All Real
Numbers will make this
equation true.
EX.8 SOLVE FOR X
3x = 3 (x+4)
MULTI-STEP EQUATION SUMMARY
3 Types
1) 1 solution
2) ∞ Solutions- Identity
3) No Solution
CLASSWORK/ HOMEWORK
Handout:
“Solving Multi-Step Equations”
You must show Work on Another
page with Justifications
Will be graded as a Classwork Grade- 10%