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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

1 answer

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).