Samuel is solving an equation for y. His first step is to add 7 to both sides. Which equation is he solving?

Question

2y - 7 = 15

2y - 15 = 7

2y + 15 = 7

2y + 7 = 15

Answer 1

To determine which equation Samuel is solving, we need to see which equation results in an addition of 7 to both sides.

Let's examine each equation:

1. Equation: \(2y - 7 = 15\)

   • If we add 7 to both sides: \[ 2y - 7 + 7 = 15 + 7 \] \[ 2y = 22 \]
   • Here, Samuel would add 7 to both sides. This works.

2. Equation: \(2y - 15 = 7\)

   • If we add 7 to both sides: \[ 2y - 15 + 7 = 7 + 7 \] \[ 2y - 8 = 14 \]
   • This does not work because the left side doesn’t simplify correctly.

3. Equation: \(2y + 15 = 7\)

   • If we add 7 to both sides: \[ 2y + 15 + 7 = 7 + 7 \] \[ 2y + 22 = 14 \]
   • This does not apply either since we added 7 incorrectly to get the same outcome.

4. Equation: \(2y + 7 = 15\)

   • If we add 7 to both sides: \[ 2y + 7 + 7 = 15 + 7 \] \[ 2y + 14 = 22 \]
   • This is also incorrect as well.

The correct conclusion is that Samuel is solving the equation \(2y - 7 = 15\), as this is the only equation that allows for the addition of 7 to both sides.