Algebra 1 Common Core Student Edition, Grade 8-9

Concept Byte

Use W ith Lesson 2 -4

Modeling Equations

With Variables on

Both Sides

Common Core State Standards

Prepares for A-REI.A.1 Explain each step in

solving a simple equation as following from the

equality of numbers asserted at the previous

step,...

MP 7

Algebra tiles can help you understand how to solve equations with variables on

both sides.

Activity

Model and solve 3b — 4 = b + 2.

Equation Algebra tiles

3b — 4 = b + 2

3b-4-b = b + 2-b

2b — 4 = 2

2b-4 + 4 = 2 + 4

2b = 6

2b _6

2 — 2

b = 3

■■■■■I SBBI _J _j

52*”

(^) mm
flBHHH HI IS
[■■■ I
warnmm^111
warn 1 .i 1 ..i
J J
111
mm in
j
Step
Model the equation using tiles.
Remove one green tile from each side of
the equation so th a t all rem aining green
tiles are on one side.
A dd fo u r y e llo w tile s to each side o f th e
equation to form zero pairs that can
be removed.
Notice that two green tiles equal six
yellow tiles. You can divide the tiles
on each side o f th e e q u a tio n in to tw o
identical groups, as shown.
So, one green tile equals th re e y e llo w
tiles. The solution o f 3b - 4 = b + 2
is b = 3. You can s u b s titu te 3 fo r b
to check.
Ex e r c i se s
Write the equation modeled by the algebra tiles.
1- Hi J^2. m n mam ■■■ J J
wmm mmm j BHHB _i _J
mam J
Use algebra tiles to model and solve each equation.

3. 3x — 5 = x + 3 4. 6x — 4 — 3x^ +^2 5. 5x^ - 3 = 3x^ +^16. 4x^ + 4 = 1 + x

c

PowerAlgebra.com | Co n c e p t B y t e Eq u a t i o n s W i t h V a r i a b l e s o n Bo t h Si d es 1 0 1