To solve the problem, let's first verify the original equation:
Given: Peter lost 3 baseball cards, so if he started with \( x \) cards, he has \( x - 3 \) cards left. Peter then gave half of his remaining cards to Bobby, which is represented as:
\[ \frac{1}{2}(x - 3) = 9 \]
Now, solving for \( x \):
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Multiply both sides by 2: \[ x - 3 = 18 \]
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Add 3 to both sides: \[ x = 21 \]
Thus, Peter started with 21 baseball cards.
Now, to verify Bobby's claim that Peter started with 21 cards, we can go through the statements:
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Substitute 21 for x in the original equation: True. This verifies whether \( x = 21 \) holds true in the equation.
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Substitute any number for x in the original equation: False. This does not verify Bobby's specific claim; it only tests if the equation holds for other values.
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Bobby’s claim that x = 21 is correct: True. We determined \( x = 21 \) is indeed correct.
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The result of verifying Bobby’s work is 9 = 9: True. When substituting \( x = 21 \) into \(\frac{1}{2}(21 - 3) = 9\), it holds true.
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The result of verifying Bobby’s work is 21 = 21: False. This statement doesn't apply to the context of verifying the original equation; instead, we compare numerical outcomes (like checking if both sides of an equation are equal).
So, the true statements about verifying Bobby’s claim are:
- Substitute 21 for x in the original equation.
- Bobby’s claim that x = 21 is correct.
- The result of verifying Bobby’s work is 9 = 9.
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