Samuel is solving an equation for y

Question

. His first step is to add 7 to both sides. Which equation is he solving?(1 point)
Responses

2y + 7 = 15
2 y plus 7 equals 15

2y − 7 = 15
2 y minus 7 equals 15

2y + 15 = 7
2 y plus 15 equals 7

2y − 15 = 7

Answer 1

To determine which equation Samuel is solving, we need to consider what happens when he adds 7 to both sides.

If he has an equation of the form \( A = B \) and adds 7 to both sides, that transforms the equation into \( A + 7 = B + 7 \).

Let's analyze the options provided:

1. 2y + 7 = 15

   • If this is the equation, adding 7 to both sides gives us:
     \( 2y + 7 + 7 = 15 + 7 \)
     \( 2y + 14 = 22 \) (not equivalent to the original equation)

2. 2y − 7 = 15

   • Adding 7 to both sides:
     \( 2y - 7 + 7 = 15 + 7 \)
     \( 2y = 22 \) (this could be valid if he simplifies further, but not matching our equation)

3. 2y + 15 = 7

   • Adding 7 to both sides:
     \( 2y + 15 + 7 = 7 + 7 \)
     \( 2y + 22 = 14 \) (not equivalent to the original equation)

4. 2y − 15 = 7

   • Adding 7 to both sides:
     \( 2y - 15 + 7 = 7 + 7 \)
     \( 2y - 8 = 14 \) (not matching)

The only logical option would have been if the initial equation was \( 2y - 7 = 8 \) (adding 7 properly) but that is not given in the choices.

None of the provided options appear to allow for a direct first transformation by adding 7, leading to the conclusion of an ambiguity. If you want to continue solving for \( y \), you might need to clarify or recheck the given equations as they don't yield a clear sequence based on the provided steps.

If forced to select an option based on the mechanics of solving, 2y - 7 = 15 would suit a logical equation form where, on addition of 7, one could directly find solutions after rearranging.