Question

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 1

1. no
2. yes
3. no
4. yes
5. yes

Step-by-step 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)