After losing 3 baseball cards, Peter gave half of his remaining cards to Bobby. If Peter gave Bobby 9 baseball cards, how many cards did Peter start with? Linear equation: (x-3) = 9 Bobby claims that Peter started with 21 cards. Which statements are true about verifying Bobby's claim? Check all that apply. Substitute 21 for x in the original equation. O Substitute any number for x in the original equation. O Bobby's claim that x = 21 is correct. The result of verifying Bobby's work is 9 = 9, The result of verifying Bobby's work is 21 = 21.

After losing 3 baseball cards, Peter gave half of his remaining cards to Bobby. If Peter gave Bobby 9 baseball cards, how many cards did Peter start with? Linear equation: (x-3) = 9 Bobby claims that Peter started with 21 cards. Which statements are true about verifying Bobby's claim? Check all that apply. Substitute 21 for x in the original equation. O Substitute any number for x in the original equation. O Bobby's claim that x = 21 is correct. The result of verifying Bobby's work is 9 = 9, The result of verifying Bobby's work is 21 = 21.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Math Problem: Solving Linear Equations Involving Baseball Cards

#### Problem Statement:
After losing 3 baseball cards, Peter gave half of his remaining cards to Bobby. If Peter gave Bobby 9 baseball cards, how many cards did Peter start with?

#### Given Linear Equation:
\[ \frac{1}{2} (x - 3) = 9 \]

#### Verification of a Claim:
Bobby claims that Peter started with 21 cards. Which statements are true about verifying Bobby's claim? Check all that apply.

- [ ] Substitute 21 for $ x $ in the original equation.
- [ ] Substitute any number for $ x $ in the original equation.
- [ ] Bobby's claim that $ x = 21 $ is correct.
- [ ] The result of verifying Bobby's work is $ 9 = 9 $.
- [ ] The result of verifying Bobby's work is $ 21 = 21 $.

### Explanation:
To verify Bobby's claim, substitute $ x = 21 $ into the original equation and check if the equation holds true.

1. Substitute $ x = 21 $ into the equation:
\[ \frac{1}{2} (21 - 3) = 9 \]
2. Simplify inside the parenthesis first:
\[ 21 - 3 = 18 \]
3. Then multiply by $\frac{1}{2}$:
\[ \frac{1}{2} \times 18 = 9 \]
4. Since the left side of the equation equals the right side (9 = 9), Bobby's claim that Peter started with 21 cards is correct.

This approach ensures that the solution is correct, and it verifies each step to confirm the final outcome.

Make sure to mark only the statements that are true based on the verification process.

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