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.
Transcribed Image Text:### 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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
![### 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.](https://content.bartleby.com/qna-images/question/9e06d118-cd7a-40d6-816b-541c8014fc69/c07c4284-741c-4bcd-acc2-13a8dee24d49/zc5tu3h_processed.jpeg)
Contemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSON
Introduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education