### Student Page 1.6.5 Combining Like Terms

#### 1.

Find the area of each of the algebra tiles shown. The side lengths are labeled. The variable, \(x\text{,}\) represents an unknown length.

#### 2.

Translate each of the figures into algebra. Explain your translation. Simplify each expression as much as possible and explain why you cannot simplify further.

##### (a)

##### (b)

##### (c)

##### (d)

#### 3.

Draw algebra tiles to illustrate each expression. Use your illustration to simplify each of the algebraic expressions. Explain how you know you are correct.

##### (a)

\(2x + 4 + 3x + 7 =\)

##### (b)

\(4x + 8 - 3x + 2 =\)

##### (c)

\(3x + 8 - (4x + 2) =\)

##### (d)

\(7x - 2(3x - 1) + x =\)

#### 4.

Summarize your work with combining like terms. Which terms can you combine? How do you know?

#### 5.

Simplify the following expressions. Show and explain your work.

##### (a)

\(3 + 5x - x + 7 =\)

##### (b)

\(3 + 5x - (x + 7) =\)

##### (c)

\(4 + 2(x - 1) =\)

##### (d)

\(15x - 4(2 - 3x) + 7 =\)