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:
- \( 15y - 1 = \frac{11}{2}y + 2 \)
To solve for \( y \), we want to isolate \( y \) on one side.
Let’s analyze the suggested options for the third step:
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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.
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Distribute 15 to each term on the left side: This is unnecessary since the left side does not have parentheses that need distributing.
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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 \( y \).
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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 \( y \).
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