Noa hopes to pick the winning ticket during her math class’s raffle. The student who picks the ticket with a true statement will win. Which is the winning ticket?

Question

4 (x minus 5) = 35 is equivalent to 4 x = 40
8 (x minus 7) = 35 is equivalent to 8 x = 28.
2 (x minus 6) = negative 35 is equivalent to 2 x = negative 23
9 (x minus 6) = negative 35 is equivalent to 9 x = negative 29

Answer 1

To find the winning ticket, we need to evaluate whether each of the given statements is true. We'll start by simplifying each equation and determining whether the equivalence stated is correct.

1. 4(x - 5) = 35 is equivalent to 4x = 40

   • Start with the left side: \[ 4(x - 5) = 4x - 20 = 35 \]
   • Rearranging gives: \[ 4x = 35 + 20 \implies 4x = 55 \]
   • This is not equivalent to \(4x = 40\). This statement is false.

2. 8(x - 7) = 35 is equivalent to 8x = 28

   • Start with the left side: \[ 8(x - 7) = 8x - 56 = 35 \]
   • Rearranging gives: \[ 8x = 35 + 56 \implies 8x = 91 \]
   • This is not equivalent to \(8x = 28\). This statement is false.

3. 2(x - 6) = -35 is equivalent to 2x = -23

   • Start with the left side: \[ 2(x - 6) = 2x - 12 = -35 \]
   • Rearranging gives: \[ 2x = -35 + 12 \implies 2x = -23 \]
   • This is equivalent to \(2x = -23\). This statement is true.

4. 9(x - 6) = -35 is equivalent to 9x = -29

   • Start with the left side: \[ 9(x - 6) = 9x - 54 = -35 \]
   • Rearranging gives: \[ 9x = -35 + 54 \implies 9x = 19 \]
   • This is not equivalent to \(9x = -29\). This statement is false.

The only statement that is true is the third one: 2(x - 6) = -35 is equivalent to 2x = -23. Therefore, the winning ticket is the third one.