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