Which of the following is equivalent to the pair of inequalities $x + 6 > 10$ and $x - 3 \leq 5$ ?

2 \leq x < 16

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2 \leq x < 4

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2 < x \leq 8

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4 < x \leq 8

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4 \leq x < 16

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Solution

The correct option is D $4 < x \leq 8$
As per given conditions,
$x + 6 > 10$ $\to$ $x > 4$
$x - 3 \leq 5$ $\to$ $x \leq 8$
So, the final relation comes out as : $4 < x \leq 8$ (option D)

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