Let's determine which value of [tex]\( x \)[/tex] from the given options satisfies the equation [tex]\( (x-3)(x-5) = 35 \)[/tex].
We will solve this by substituting each given value into the equation and checking if the equation holds true.
1. For [tex]\( x = -8 \)[/tex]:
[tex]\[
(x-3)(x-5) \Rightarrow (-8-3)(-8-5) = (-11)(-13) = 143
\][/tex]
Which is not equal to 35.
2. For [tex]\( x = -5 \)[/tex]:
[tex]\[
(x-3)(x-5) \Rightarrow (-5-3)(-5-5) = (-8)(-10) = 80
\][/tex]
Which is not equal to 35.
3. For [tex]\( x = 2 \)[/tex]:
[tex]\[
(x-3)(x-5) \Rightarrow (2-3)(2-5) = (-1)(-3) = 3
\][/tex]
Which is not equal to 35.
4. For [tex]\( x = 10 \)[/tex]:
[tex]\[
(x-3)(x-5) \Rightarrow (10-3)(10-5) = (7)(5) = 35
\][/tex]
This is equal to 35.
So the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( (x-3)(x-5) = 35 \)[/tex] is [tex]\( x = 10 \)[/tex].
