Priscilla has a number riddle for her friends. She wants them to guess what number she is thinking of. She tells them that her number can be represented by the x

Question

in the equation 3x−10=26
. Her friends guess {6, 12, 13, 36}
. Using substitution, which guess was the correct number?(1 point)
Responses

36
36

12
12

13
13

6

Answer 1

To find the correct number Priscilla is thinking of, we need to solve the equation \(3x - 10 = 26\).

1. Start by isolating the term with \(x\): \[ 3x - 10 + 10 = 26 + 10 \] \[ 3x = 36 \]

2. Now, divide by 3: \[ x = \frac{36}{3} = 12 \]

So, the number Priscilla is thinking of is 12. We can verify this by substituting each guess into the equation \(3x - 10 = 26\):

• For \(x = 6\): \[ 3(6) - 10 = 18 - 10 = 8 \quad (\text{not correct}) \]

• For \(x = 12\): \[ 3(12) - 10 = 36 - 10 = 26 \quad (\text{correct}) \]

• For \(x = 13\): \[ 3(13) - 10 = 39 - 10 = 29 \quad (\text{not correct}) \]

• For \(x = 36\): \[ 3(36) - 10 = 108 - 10 = 98 \quad (\text{not correct}) \]

The correct guess is 12.