Algebra 1 Common Core Student Edition, Grade 8-9

(Marvins-Underground-K-12) #1
Getting Ready!

Th e diagram shows t h e amount o f money t h at each p layer st ar t s wit h
in a video game. To be f a i r , each p layer should have t he same amount
of money. What amount must be in the chest? How do you know?

@ Common Core State Standards
A-CED.A.1 Create equations... in one variable and use
them to solve problems. Include equations arising from
lin e a r ... functions. Also A-REI.B.3
MP 1, M P 3 , MP 4, MP 7

Objective T o s o lv e o n e - s te p e q u a t io n s i n o n e v a r ia b le

Solving One-Step


Equations


Fi r st make a plan
f o r how you ar e
going t o solve t his
problem.

MAtHEMAtlCAL
PRACTICES

Player 1 Player 2

Lesson
Vocabulary
equivalent
equations


  • A d dition
    Property of
    Equality

  • Subtraction
    Property of
    Equality

  • isolate

  • inverse
    operations

  • M ultiplication
    Property of
    Equality

  • Division Property
    of Equality


I n th e S o lv e It, y o u m a y h a v e u s e d r e a s o n in g to f i n d th e a m o u n t o f m o n e y i n th e c h e s t.
In this lesson, you w ill learn to solve problem s like the one above by using equations.

Esse n t i a l U n d e r st a n d i n g Equivalent equations a re e q u a t io n s t h a t h a v e th e
s a m e s o lu t io n ( s ). Y o u c a n f i n d th e s o lu t io n o f a o n e - s te p e q u a t io n u s in g t h e p r o p e r t ie s
o f e q u a lit y a n d in v e r s e o p e r a t io n s to w r it e a s im p le r e q u iv a le n t e q u a t io n.

Pr o p er t y Addition and Subtraction Properties of Equality


Addition Property of Equality A d d in g t h e s a m e n u m b e r t o e a c h s id e o f a n e q u a t io n
produces an equivalent equation.
Algebra Example
For any real num bers a, b, and c,
if a = b, then a + c = b + c.

x — 3 = 2
x — 3 + 3 = 2 + 3

Subtraction Property of Equality S u b t r a c t in g t h e s a m e n u m b e r f r o m e a c h s id e o f a n
equation produces an equivalent equation.
Algebra
For any real num bers a, b, and c,
ifa = b, th e n a — c = b — c.

Example
X+ 3 = 2
x + 3 — 3 = 2

I


PowerAlgebra.com ^ | Lesson 2-1 Solving One-Step Equations 81
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