Question

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

Answer 1

Answer:

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

Step-by-step 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 $\mathbf{x>1 \ or \ x<-3}$