The solution set of the inequation x 2 + 6 x - 7 | x + 4 | 0 is

Question

The solution set of the inequation $\frac{x^{2} + 6 x - 7}{| x + 4 |} < 0$ is

Smart Achievers · Accepted Answer

(4)

$Given inequation is$

$\frac{x^{2} + 6 x - 7}{| x + 4 |} < 0$ ...(i)

Since $| x + 4 | > 0$ $\forall x \in R except for x = - 4$

$∵$ $for x = - 4, (i) does not exist.$

$∴$ $x^{2} + 6 x - 7 < 0 for given inequation$

$or x^{2} + 7 x - x - 7 < 0$

$or (x + 7) (x - 1) < 0 or x \in (- 7, 1)$

$∴$ $Solution set of (i) is (- 7, - 4) \cup (- 4, 1)$

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