Question

Which equation has no solution? A. X-5(x-4) = 2(2x + 7) + 6 B. 5(x + 1)-3x = 5-2(5-x) C. 1-3(x + 3) = 2(3x - 4) - 9x D. 3(x-4) + x = 4(3-x)

Answer 1

Answer:

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

Step-by-step explanation:

A. x - 5(x - 4) = 2(2x + 7) + 6        Distribute -5 into parentheses

   x - 5x + 20 = 2(2x +7) + 6        Distribute 2 into parentheses

   x - 5x + 20 = 4x +14 + 6           Combine like terms (I underlined it to show)

   -4x + 20 = 4x + 20

   +4x           +4x                            Do Inverse operations

         20  = 8x + 20

        -20          - 20                       Do inverse operations

         0 = 8x

         $\frac{0}{8}$ = $\frac{8x}{8}$                           Divide by 8 on both sides to isolate the variable.

        0 = x

Solution is x = 0.

B. 5(x + 1) - 3x = 5 - 2(5 - x)           Distribute 5 into parentheses

   5x + 5 - 3x = 5 - 2(5 - x)            Distribute -2 into parentheses

   5x + 5 - 3x = 5 - 10 + 2x    Combine Like terms (I underlined the like terms)

   2x + 5 = -5 + 2x                        

        + 5    +5                               Do inverse operations

  2x + 10 = 2x    

 -2x          -2x                               Do inverse operations

          10 ≠ 0

No solution

C. 1 - 3(x+3) = 2(3x - 4) - 9x          Distribute -3 into parentheses

   1 - 3x - 9 = 2(3x - 4) - 9x           Distribute 2 into parentheses

   1 - 3x - 9 = 6x - 8 - 9x       Combine Like terms (I underlined the like terms)

   - 8 - 3x = -3x - 8              

        + 3x   +3x                            Do inverse operations

        - 8 = - 8

Solution = All real numbers

D.  3(x - 4) + x = 4(3 - x)               Distribute 3 into parentheses

     3x - 12 + x = 4(3 - x)                Distribute 4 into parentheses

     3x - 12 + x = 12 - 4x         Combine Like terms (I underlined the like terms)

     4x - 12 = 12 - 4x    

    +4x              + 4x                      Do inverse operations

    8x - 12 = 12  

        + 12  +12                              Do inverse operations

     8x  = 24  

     $\frac{8x}{8}$   = $\frac{24}{8}$                       Divide by 8 on both sides to isolate the variable

    x = 3

Solution is x = 3 .    

So the only equation that has no solution is B. 5(x + 1) - 3x = 5 - 2(5 - x).