Question

Which equation has no solution?

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

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

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

D) 4 +672 + x) = 2(3x + 8)

Answer 1

B

Explanation:

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

simplify

5 + 6 + 4x = x + 3x + 3

simplify once more

11 + 4x = 4x + 3

subtract 3 from both sides

8 + 4x = 4x

divide by 4

2 + x = x

no solution, because it is saying x equals something larger than x

Answer 2

Answer: B) 5 + 2(3 + 2x) = x + 3(x + 1)

Explanation:

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

4x + 12 + 2x = 6x + 12

6x + 12 = 6x + 12

infinitely many solutions

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

5 + 6 + 4x = x + 3x + 3

11 + 4x = 4x + 3

11 = 3

FALSE

No Solution

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

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

15 + 6x = 4x + 15

15 + 2x = 15

2x = 0

x = 0

One Solution

D) 4 + 672 + x = 2(3x + 8)

676 + x = 6x + 16

660 = 5x

180 = x

One Solution