Algebra 1 Common Core Student Edition, Grade 8-9

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