Given that $- 7 < - 3 x + 5 \leq 20$ , the least possible value which the expression $6 x + 1$ can take is:

- 28

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29

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25

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- 29

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Solution

The correct option is D $- 29$
Given that $- 7 < - 3 x + 5 \leq 20$
$\Rightarrow - 7 - 5 < - 3 x \leq 20 - 5$
$\Rightarrow - 12 < - 3 x \leq 15$
$\Rightarrow 12 > 3 x \geq - 15$
$\Rightarrow 4 > x \geq - 5$
Since we need the least possible value of $6 x + 1, x$ must be substituted as $- 5$ , thus giving the value to be $- 30 + 1 = - 29$

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