Question

Find the sum of integer values that satisfy x^2 + 6x-7<0.
1- -24
2- -21
3- -18
4- -27​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Find the sum of integer values that satisfy

$\sf{ {x}^{2} + 6x - 7 < 0}$

1. - 24

2. - 21

3. - 18

4. - 27

EVALUATION

Here the given inequality is

$\sf{ {x}^{2} + 6x - 7 < 0}$

We now solve for x

$\sf{ {x}^{2} + 6x - 7 < 0}$

$\sf{ \implies {x}^{2} + (7 - 1)x - 7 < 0}$

$\sf{ \implies {x}^{2} + 7x - x - 7 < 0}$

$\sf{ \implies x(x + 7) - 1(x + 7) < 0}$

$\sf{ \implies (x + 7) (x - 1) < 0}$

$\sf{ \implies \: - 7 < x < 1}$

Since x is an integer

∴ x = - 6 , - 5 , - 4 , - 3 , - 2 , - 1 , 0

Hence the required sum

= - 6 - 5 - 4 - 3 - 2 - 1 + 0

= - 21

FINAL ANSWER

Hence the correct option is 2. - 21

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