Determine where the values 4 and 6 are solutions to the quadratic equation 22 - 10г + 24, and then select the correct answer from the following options. (1 point)

• Neither x=4 nor x=6 is a solution.
• Only x=6 is a solution
• Both x=4 and x=6 are solutions
• Only x=4 is a solution

1 answer

To determine if the values \( x = 4 \) and \( x = 6 \) are solutions to the quadratic equation represented as \( 22 - 10x + 24 = 0 \), we first need to simplify the equation.

  1. Combine like terms: \[ 22 + 24 - 10x = 0 \] \[ 46 - 10x = 0 \]

  2. Rearranging this gives: \[ 10x = 46 \] \[ x = \frac{46}{10} = 4.6 \]

Now, we will check both values:

  • For \( x = 4 \): \[ 46 - 10(4) = 46 - 40 = 6 \quad (\text{not } 0) \]

  • For \( x = 6 \): \[ 46 - 10(6) = 46 - 60 = -14 \quad (\text{not } 0) \]

Since neither \( x = 4 \) nor \( x = 6 \) satisfies the equation \( 22 - 10x + 24 = 0 \), we find:

The correct answer is: Neither \( x = 4 \) nor \( x = 6 \) is a solution.