$- 8 > 2 x + 10 + 6 x > - 20$ , Which is the possible range of values of 4x + 5?

Any value greater than - 4 or less than -10

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Any value greater than -10 and less than - 4

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Any value greater than

- \frac{9}{4}

or less than

- \frac{15}{4}

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Any value greater than

- \frac{15}{4}

or less than

- \frac{9}{4}

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Solution

The correct option is B Any value greater than -10 and less than - 4
$- 8 > 2 x + 10 + 6 x > - 20$
$- 8 > 8 x + 10 > - 20$

Dividing by 2 on each side $- \frac{8}{2} > \frac{8 x + 10}{2} > - \frac{20}{2} - 4 > 4 x + 5 > - 10$

The possible range of 4x + 5 is any value greater than -10 and less than -4

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