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: [tex] \frac{1}{2}(x-3)=9 [/tex]

Bobby claims that Peter started with 21 cards. Which statements are true about verifying Bobby's claim? Check all that apply.

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



Answer :

Let's verify Bobby's claim step by step by using the information provided and analyzing the equations and results carefully.

1. Substitute 21 for \( x \) in the original equation:

The original equation is:

[tex]\[ \frac{1}{2}(x - 3) = 9 \][/tex]

Substitute \( x = 21 \):

[tex]\[ \frac{1}{2}(21 - 3) = \frac{1}{2}(18) = 9 \][/tex]

This substitution holds true as:

[tex]\[ 9 = 9 \][/tex]

Hence, substituting 21 for \( x \) in the original equation verifies the claim correctly.

2. Substitute any number for \( x \) in the original equation:

In general, you can substitute any number for \( x \), but it may not satisfy the equation. Here, we are specifically testing for \( x = 21 \) to verify Bobby’s claim.

3. Bobby's claim that \( x = 21 \) is correct:

Since:

[tex]\[ \frac{1}{2}(21 - 3) = 9 \][/tex]

And simplifying gives:

[tex]\[ \frac{1}{2}(18) = 9 \][/tex]

Which results in:

[tex]\[ 9 = 9 \][/tex]

This indicates that Bobby’s claim is indeed correct. Therefore, Peter started with 21 cards.

4. The result of verifying Bobby's work is \( 9 = 9 \):

From the verification steps we see:

[tex]\[ \frac{1}{2}(21 - 3) = 9 \][/tex]

Results in:

[tex]\[ 9 = 9 \][/tex]

Hence, \( 9 = 9 \) is a true statement validating Bobby's work.

5. The result of verifying Bobby's work is \( 21 = 21 \):

This is not applicable in the context of the original equation, as there is no step in the verification that directly results in \( 21 = 21 \). Therefore, this statement is false.

In summary:
- \( \boxed{\text{Substitute 21 for } x \text{ in the original equation.}} \)
- \( \boxed{\text{Bobby's claim that } x = 21 \text{ is correct.}} \)
- \( \boxed{\text{The result of verifying Bobby's work is } 9 = 9.} \)

The other statements do not apply in verifying Bobby's claim.