Concept Byte: Modeling Equations With Variables on Both Sides

Use With Lesson 2-4

ACTIVITY

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

Activity

Model and solve 3 b − 4 = b + 2 . 3 b minus 4 equals b plus 2 .

Equation	Algebra tiles	Step
3 b − 4 = b + 2 3 b minus 4 equals b plus 2		Model the equation using tiles.
3 b − 4 − b = b + 2 − b 2 b − 4 = 2 table with 2 rows and 2 columns , row1 column 1 , 3 b minus 4 minus b , column 2 equals b plus 2 minus b , row2 column 1 , 2 b minus 4 , column 2 equals 2 , end table		Remove one green tile from each side of the equation so that all remaining green tiles are on one side.
2 b − 4 + 4 = 2 + 4 2 b = 6 table with 2 rows and 2 columns , row1 column 1 , 2 b minus 4 plus 4 , column 2 equals 2 plus 4 , row2 column 1 , 2 b , column 2 equals 6 , end table		Add four yellow tiles to each side of the equation to form zero pairs that can be removed.
2 b 2 = 6 2 fraction 2 b , over 2 end fraction , equals , 6 halves		Notice that two green tiles equal six yellow tiles. You can divide the tiles on each side of the equation into two identical groups, as shown.
b = 3		So, one green tile equals three yellow tiles. The solution of 3 b − 4 = b + 2 3 b minus 4 equals b plus 2  is b = 3. You can substitute 3 for b to check.

Exercises

Write the equation modeled by the algebra tiles.

Use algebra tiles to model and solve each equation.

3. 3 x − 5 = x + 3 3 x minus 5 equals x plus 3
4. 6 x − 4 = 3 x + 2 6 x minus 4 equals 3 x plus 2
5. 5 x − 3 = 3 x + 1 5 x minus 3 equals 3 x plus 1
6. 4x + 4 = 1 + x

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