Question

If (x + 1)(x - 5) = -9, then which of the following statements is true?x+1= 0 or x-5 = 0x+1=-9 or x-5=-9X-2 = 0

Answer 1

Given:

(x + 1)(x - 5) = -9

Let's select the correct statement from the given options.

Equate the equation to zero by adding 9 to both sides of the equation:

(x + 1)(x- 5) + 9 = -9 + 9

(x + 1)(x - 5) + 9 = 0

Expand the left side using FOIL method:

`x(x-5)+1(x-5)+9=0`

Apply distributive property:

`x^2-5x+x-5+9=0`

Combine like terms:

`x^2-4x+4=0`

Factor using the perfect square rule:

`\begin{gathered} x^2-2\ast x\ast2+2^2=0 \\ \\ (x-2)^2=0 \end{gathered}`

Thus, we have the factor:

`x-2=0`

Therefore, the correct statement is: x - 2 = 0

ANSWER:

x - 2 = 0