Question

Samuel is solving an equation for y . 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 − 15 = 7
2 y minus 15 equals 7

2y − 7 = 15
2 y minus 7 equals 15

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

Answer 1

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

1. **If the equation is \(2y + 7 = 15\)**: By subtracting 7 from both sides, we have:
\[2y + 7 - 7 = 15 - 7 \Rightarrow 2y = 8\]
So adding 7 to both sides is appropriate at this step.

2. **If the equation is \(2y - 15 = 7\)**: By adding 15 to both sides, we have:
\[2y - 15 + 15 = 7 + 15 \Rightarrow 2y = 22\]
This equation does not work with adding 7.

3. **If the equation is \(2y - 7 = 15\)**: By adding 7 to both sides, we have:
\[2y - 7 + 7 = 15 + 7 \Rightarrow 2y = 22\]
This equation works with adding 7.

4. **If the equation is \(2y + 15 = 7\)**: By subtracting 15 from both sides, we have:
\[2y + 15 - 15 = 7 - 15 \Rightarrow 2y = -8\]
This equation does not work with adding 7.

The only valid equations where adding 7 to both sides makes sense for Samuel's first step are the first and third equations. However, the third equation \(2y - 7 = 15\) needs a different operation than adding 7.

Thus, the best choice is:

**\(2y + 7 = 15\)** (first equation).