Algebraic expressions

Advanced Math 6 · Unit 8 · algebraic-expressions-6 · Teacher edition

algebraic-expressions-6

Name ______________________________Date ______________

1.
Evaluate $3x + 2$ when $x = 4$ .
Answer: ______________
2.
Which expression is equivalent to $3(2x + 4) + x$ ?
1. (A)
  $6x + 4$
2. (B)
  $7x + 12$
3. (C)
  $6x + 12$
4. (D)
  $7x^2 + 12$
3.
Simplify $3(2x + 4) + x$ , then evaluate it at $x = \dfrac{1}{2}$ .
Answer: ______________
4.
Simplify $5y + 3 - 2y + 7$ .
1. (A)
  $7y + 10$
2. (B)
  $13y$
3. (C)
  $3y + 10$
4. (D)
  $3y^2 + 10$
5.
Factor $12x + 18$ by taking out the greatest common factor.
1. (A)
  $2(6x + 9)$
2. (B)
  $3(4x + 6)$
3. (C)
  $6(2x + 3)$
4. (D)
  $6(2x + 18)$

Answer key — Algebraic expressions

1.
14algebraic-expressions-6-01
$3(4) + 2 = 12 + 2 = \mathbf{14}$ . (Writing $34 + 2$ is the classic slip.)
2.
(B)
$7x + 12$
algebraic-expressions-6-02
$3(2x+4) + x = 6x + 12 + x = \mathbf{7x + 12}$ . ( $6x + 4$ forgets to distribute to the $4$ ; $6x + 12$ forgets the extra $x$ ; $7x^2$ multiplies $x$ -terms instead of adding them.)
3.
15.5algebraic-expressions-6-03
$7x + 12$ at $x = \frac{1}{2}$ : $3.5 + 12 = \mathbf{15.5}$ . Check without simplifying: $3(1 + 4) + 0.5 = 15 + 0.5 = 15.5$ . ✓
4.
(C)
$3y + 10$
algebraic-expressions-6-04
$5y - 2y = 3y$ and $3 + 7 = 10$ , so $\mathbf{3y + 10}$ . ( $13y$ mixes numbers into the $y$ -term; $7y$ adds instead of subtracting.)
5.
(C)
$6(2x + 3)$
algebraic-expressions-6-05
$12x + 18 = \mathbf{6(2x + 3)}$ . Check by distributing: $6 \cdot 2x + 6 \cdot 3 = 12x + 18$ ✓. $2(6x+9)$ and $3(4x+6)$ are true but not fully factored; $6(2x + 18)$ expands to $12x + 108$ .