Question

Verifying a Solution

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:  12 (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.

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.

Answer 1

True:
- Substitute 21 for x in the original equation. (To verify a claimed solution you plug it into the equation.)
- Bobby’s claim that x = 21 is correct. (Solving (1/2)(x − 3) = 9 gives x = 21.)
- The result of verifying Bobby’s work is 9 = 9. ((1/2)(21 − 3) = (1/2)(18) = 9.)

False:
- Substitute any number for x in the original equation. (You must substitute the claimed value to verify it.)
- The result of verifying Bobby’s work is 21 = 21. (You get 9 = 9, not 21 = 21.)

(Note: the printed "12(x − 3) = 9" appears to be a typo for (1/2)(x − 3) = 9.)