Question

Which equation has no solution?

Answer 1

Answer:

B

Step-by-step 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)

Step-by-step 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