Re: Inequality with absolute values

Answer Should be C

First of all, equation within Modulus can not be negative. So |x+4| has to be positive.

Now if \frac{a}{b} is negative and b is positive, then a must be negative. i.e. x^2 + 6x - 7 < 0

So we have that x^2 + 6x - 7 < 0 --------> (x+7)(x-1) < 0 -------> Now we get three ranges of x
1) x < -7
2) -7 < x < 1
3) x > 1
Here we can see that the range mentioned in serial number 2 satisfies the inequality (x+7)(x-1) < 0. So -7 < x < 1

Now let's work on denominator. We know that |x+4| > 0 --------> x > -4 or x < -4 that means x is not equal to -4 -------[ |x-a| > r then x > a+r or x < a-r ]

Consider both the ranges together
-7 < x < 1 and x is not equal to -4
So -7 < x < -4 and -4 < x < 1

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Hope that helps