Which is a solution to the equation?

[tex]\[
(x-3)(x-5) = 35
\][/tex]

A. [tex]\(x = -8\)[/tex]

B. [tex]\(x = -5\)[/tex]

C. [tex]\(x = 2\)[/tex]

D. [tex]\(x = 10\)[/tex]



Answer :

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].