To determine which value of [tex]\( x \)[/tex] is a solution to the equation [tex]\( (x-3)(x-5) = 35 \)[/tex], we will substitute each given value into the equation and check if it satisfies the equation.
The values to test are [tex]\( x = -8 \)[/tex], [tex]\( x = -5 \)[/tex], [tex]\( x = 2 \)[/tex], and [tex]\( x = 10 \)[/tex].
1. Testing [tex]\( x = -8 \)[/tex]:
Substitute [tex]\( x = -8 \)[/tex] into the equation:
[tex]\[
(-8-3)(-8-5) = (-11)(-13)
\][/tex]
[tex]\[
(-11)(-13) = 143
\][/tex]
Since 143 is not equal to 35, [tex]\( x = -8 \)[/tex] is not a solution.
2. Testing [tex]\( x = -5 \)[/tex]:
Substitute [tex]\( x = -5 \)[/tex] into the equation:
[tex]\[
(-5-3)(-5-5) = (-8)(-10)
\][/tex]
[tex]\[
(-8)(-10) = 80
\][/tex]
Since 80 is not equal to 35, [tex]\( x = -5 \)[/tex] is not a solution.
3. Testing [tex]\( x = 2 \)[/tex]:
Substitute [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[
(2-3)(2-5) = (-1)(-3)
\][/tex]
[tex]\[
(-1)(-3) = 3
\][/tex]
Since 3 is not equal to 35, [tex]\( x = 2 \)[/tex] is not a solution.
4. Testing [tex]\( x = 10 \)[/tex]:
Substitute [tex]\( x = 10 \)[/tex] into the equation:
[tex]\[
(10-3)(10-5) = (7)(5)
\][/tex]
[tex]\[
(7)(5) = 35
\][/tex]
Since 35 is equal to 35, [tex]\( x = 10 \)[/tex] is a solution.
Therefore, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( (x-3)(x-5) = 35 \)[/tex] is [tex]\( x = 10 \)[/tex].
