Question

Simplify PLEASE HELP ASAP

Answer 1

`0 < x < 6`

Explanation:

This question asks to solve an inequality which can be written as:

`√(x^2-6x+9) < 3`

Solve for x:

`√(x^2-6x+9) < 3\\x^2-6x+9 < 9\\x^2-6x < 0\\x(x-6) < 0`

From here we can deduce that the inequality is
`0` when:

`x = 0` or
`x = 6`

We can write the solution as:

`0 < x < 6`

Answer 2

`\qquad\qquad\huge\underline{{\sf Answer}}`

Let's evaluate ~

`\qquad \sf  \dashrightarrow \: \sqrt{ {x}^(2) - 6x + 9 }`

`\qquad \sf  \dashrightarrow \: \sqrt{ {x}^(2) - 3x - 3x+ 9 }`

`\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{}(x - 3) - 3(x - 3) }`

`\qquad \sf  \dashrightarrow \: √( (x - 3)(x - 3) )`

`\qquad \sf  \dashrightarrow \: \sqrt{ (x - 3) {}^(2) }`

`\qquad \sf  \dashrightarrow \: { (x - 3) {}^{} }`

Now, we have been given that value of x :

`\qquad \sf  \dashrightarrow \:x < 3`

So, let's plug the value of x as 3 in the given expression ~

`\qquad \sf  \dashrightarrow \:3 - 3`

`\qquad \sf  \dashrightarrow \:0`

Therefore, we can conclude that :

`\qquad \sf  \dashrightarrow \: \sqrt{ {x}^(2) - 6x + 9 } < 0`

Value of the expression should be less than 0