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A moving company weighs 25 boxes
you have packed that contain either
books or clothes and says the total
weight is 414 pounds. You know that
a box of books weighs 30 pounds and
a box of clothes weighs 6 pounds. How
many boxes of books and how many
boxes of clothes did you pack?
Why do you think
moving companies
weigh the boxes?
GOOD AFTERNOON!
Just for fun
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%