Question

Find the range value of x which satistfy inequality (x + 2)² > 2x + 7

Answer 1

the range value of x which satisfy inequality
`(x + 2)^2 > 2x + 7` is
`\mathbf{x>1 \ or \ x<-3}`

Explanation:

We need to find the range value of x which satisfy inequality
`(x + 2)^2 > 2x + 7`

Solving:

`(x + 2)^2 > 2x + 7`

Using formula:
`(a+b)^2=a^2+2ab+b^2`

`x^2+4x+4>2x+7\\x^2+4x+4-2x-7>0\\x^2+4x-2x+4-7>0\\x^2+2x-3>0`

Now factoring the term:
`x^2+2x-3>0`

Breaking the middle term: 2x= 3x-x

`x^2+2x-3>0\\x^2+3x-x-3>0\\x(x+3)-1(x+3)>0\\(x-1)(x+3)>0\\x-1>0 \ or \ x+3>0\\x>1 \ or \ x<-3`

So, the range value of x which satisfy inequality
`(x + 2)^2 > 2x + 7` is
`\mathbf{x>1 \ or \ x<-3}`