Choose yes or no to tell if each pair of expressions is equivalent. YES OR NO

3x + 1/4 - x + 1 1/2 and 4x + 1 3/4

2 + 6x and 2 (3x+1)

3 (x+1) - (1+x) and 2x+3

3x and 4 (x+1) - x - 4

5.5 + 2.1x + 3.8x - 4.1 and 1.4 + 5.9x

Answer: no yes no yes yes Explanation:

The distributive property is useful both for collecting terms and for eliminating parentheses.

1. 3x + 1/4 - x + 1 1/2 = x (3 - 1) + (1/4 + 1 2/4) = 2x + 1 3/4 ≠ 4x + 1 3/4 (no)

2. 2 (3x+1) = 2·3x + 2·1 = 6x + 2 = 2 + 6x (yes)

3. 3 (x+1) - (1+x) = (x+1) (3 - 1) = 2 (x+1) = 2x + 2 ≠ 2x + 3 (no)

4. 4 (x+1) - x-4 = 4x + 4 - x - 4 = x (4-1) + (4-4) = 3x + 0 = 3x (yes)

5. 5.5 + 2.1x + 3.8x - 4.1 = x (2.1 + 3.8) + (5.5 - 4.1) = 5.9x + 1.4 = 1.4 + 5.9x (yes)