Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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]

Sagot :

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].