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

1 Answer

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Answer:

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}

User Mateusppereira
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