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To determine if \( x = 4 \) and \( x = 6 \) are solutions to the quadratic equation \( x^2 - 10x + 24 = 0 \), we can substitute these values into the equation and check if they satisfy it.
1. **For \( x = 4 \)**:
\[
x^2 - 10x + 24 = 4^2 - 10(4) + 24
\]
\[
= 16 - 40 + 24
\]
\[
= 16 - 40 + 24 = 0
\]
So, \( x = 4 \) is a solution.
2. **For \( x = 6 \)**:
\[
x^2 - 10x + 24 = 6^2 - 10(6) + 24
\]
\[
= 36 - 60 + 24
\]
\[
= 36 - 60 + 24 = 0
\]
So, \( x = 6 \) is a solution.
Since both \( x = 4 \) and \( x = 6 \) satisfy the equation \( x^2 - 10x + 24 = 0 \), the correct response is:
**Both x=4 and x=6 are solutions.**