Question

Examine the first two steps used to solve the equation.

3
4
(20y − 8) + 5 = 1
2
y + 1
4
(20y + 8)


1. 15y − 6 + 5 = 1
2
y + 5y + 2

2. 15y − 1 = 11
2
y + 2

Which would be a good third step to solve the equation?
Combine like terms StartFraction 11 Over 2 EndFractiony and 2.

Distribute 15 to each term on the left side.
Subtract StartFraction 11 Over 2 EndFractiony from each side of the equation.
Divide each side of the equation by 2.

Answer 1

To determine a good third step in the solution of the equation, let's first clarify what has happened in the first two steps provided.

**Step 1:** \( 15y - 6 + 5 = \frac{11}{2}y + 2 \) simplifies to \( 15y - 1 = \frac{11}{2}y + 2 \) in Step 2.

Now we have:

1. \( 15y - 1 = \frac{11}{2}y + 2 \)

To solve for \( y \), we want to isolate \( y \) on one side.

Let’s analyze the suggested options for the third step:

1. **Combine like terms \( \frac{11}{2}y \) and \( 2 \)**: This does not apply as these terms are not on the same side of the equation.

2. **Distribute 15 to each term on the left side**: This is unnecessary since the left side does not have parentheses that need distributing.

3. **Subtract \( \frac{11}{2}y \) from each side of the equation**: This is a good step because it will allow us to consolidate the terms involving \( y \) on one side, making it easier to isolate \( y \).

4. **Divide each side of the equation by 2**: This could be a viable option later but is not the best immediate step because the goal is usually to eliminate \( y \) terms on one side first.

### Conclusion:

The best third step is to **subtract \( \frac{11}{2}y \) from each side of the equation**. This will help consolidate the \( y \) terms and move towards isolating \( y \).