The number of integers which satisfy the inequality $5 < x \leq 13$ is

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Solution

$5 < x \leq 13$ is a combination of $5 < x$ and $x \leq 13.$

$5 < x$ can also be written as $x > 5$ which represents the numbers greater than 5.
$x \leq 13$ represents the numbers less than or equal to $13$ .

Hence, $5 < x \leq 13$ represents the numbers greater than $5$ and less than or equal to $13$ .

Integers that satisfy the given inequality are $6, 7, 8, 9, 10, 11, 12, 13.$
Hence, required number of integers is $8.$

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