Question

Which equation has no solution?

O 4(x + 3) + 2x = 6(x + 2)
O 5+2(3 + 2x) = x + 3(x + 1)
O 5(x + 3) + x = 4(x + 3) + 3
O 4 + 6(2 + x) = 2(3x + 8)

Answer 1

The equation which has no solution is 5 + 2(3 + 2x) = x + 3(x + 1) . (see below for work)

Explanation:

4(x + 3) + 2x = 6(x + 2)

4x + 12 + 2x = 6(x + 12)

4x + 2x = 6x

6x = 6x

x ∈ ℝ

5 + 2(3 + 2x) = x + 3(x + 1)

5 + 6 + 4x = x + 3(x + 3)

11 + 4x = x + 3x + 3

11 + 4x = 4x + 3

11 = 3

x ∈ ∅ (CORRECT ANSWER)

5(x + 3) + x = 4(x + 3) + 3

5x + 15 + x = 4x + 12 + 3

6x + 15 = 4x + 12 + 3

6x + 15 = 4x + 15

6x = 4x

6x - 4x = 0

2x = 0

x = 0

4 + 6(2 + x) = 2(3x + 8)

4 + 12 + 6x = 6x + 16

4 ÷ 12 = 16

16 = 16

x ∈ ℝ

Hope this helps! :)