Question

Задача 4. Сколько целых чисел удовлетворяет неравенству |x-3,5|⩽10? Задача 5. Сколько целых чисел удовлетворяет неравенству |x-7⅓|>2?Задача 6. Существуют ли значения a, при которых неравенству |x+a|<3 удовлетворяет ровно 7 целых чисел? Решение запишите в тетрадь. ​

Answer 1

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Answer 2

Problem 4: How many integers satisfy the inequality |x-3.5|⩽10?

To solve this problem, we need to find the range of values for x that satisfy the given inequality. Let's break it down into two cases:

Case 1: x-3.5⩽10 In this case, we have: x-3.5⩽10 x⩽10+3.5 x⩽13.5

Case 2: -(x-3.5)⩽10 In this case, we have: -(x-3.5)⩽10 -x+3.5⩽10 -x⩽10-3.5 -x⩽6.5

Now, let's solve each case separately:

Case 1: x⩽13.5 To find the number of integers that satisfy this inequality, we need to count the integers from negative infinity up to 13.5. Since we are dealing with integers, we can round down 13.5 to the nearest integer, which is 13. Therefore, there are 14 integers that satisfy this inequality.

Case 2: -x⩽6.5 To find the number of integers that satisfy this inequality, we need to count the integers from negative infinity up to 6.5. Since we are dealing with integers, we can round up 6.5 to the nearest integer, which is 7. Therefore, there are 8 integers that satisfy this inequality.

Now, to find the total number of integers that satisfy the original inequality, we need to find the intersection of the two cases. Since we are looking for integers that satisfy both x⩽13.5 and -x⩽6.5, we need to find the smaller range of values that satisfies both inequalities. In this case, the smaller range is x⩽6.5. Therefore, there are 7 integers that satisfy the original inequality.

Answer: There are 7 integers that satisfy the inequality |x-3.5|⩽10.