Consider the following equation.

-16p + 37 = 49 - 21p

select the equation that has the same solution as the given equation.

a: -14 + 6p = -9 - 6p

b: -55 + 12p = 5p + 16

c: 2 + 1.25p = 3.75p + 10

d: 3/2p - 5 + 9/4p = 7 - 5/4p

if you could also explain how to do this.

D.  3/2p - 5 + 9/4p = 7 - 5/4p

Step-by-step explanation:

We are given the equation;

-16p + 37 = 49 - 21p

We are supposed to identify the equation that has similar solution with the equation given;

-16p + 37 = 49 - 21p

Combining the like terms;

-16p + 21p = 49 - 37

 5p = 12

   p = 2.4

Solution for the choices given;

A.  -14 + 6p = -9 - 6p

     6p + 6p = -9 +14

      12p = 5

         p= 0.417

B. -55 + 12p = 5p + 16

    12p - 5p = 16 + 55

       7p = 71

         p = 10.14

C. 2 + 1.25p = 3.75p + 10

    1.25p - 3.75p = 10 - 2

             -2.5p = 8

                p = -3.2

D.  3/2p - 5 + 9/4p = 7 - 5/4p

     3/2p +5/4p +9/4p = 7 + 5

               5p =12

                     p = 2.4

Therefore, the equation that has similar equation with the one given is D. 3/2p - 5 + 9/4p = 7 - 5/4p