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Answer :
Final answer:
The number of integers that satisfy the inequality -102 ≤ x ≤ 105 is 208, which includes both -102 and 105.
Explanation:
To find the number of integers that satisfy this inequality -102 ≤ x ≤ 105, you need to simply count the integers from -102 to 105, inclusive. Therefore, you begin at -102 and go all the way up to 105. This includes both -102 and 105.
To do this, you can subtract the two boundary numbers (-102 and 105), then add 1 (because we're including both boundaries). This gives us: 105 - (-102) + 1 = 105 + 102 + 1 = 208.
So, there are 208 integers that satisfy the inequality -102 ≤ x ≤ 105.
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