Question

How many integers are solutions of the inequality |x|<4

Answer 1

There are seven integers that satisfy the inequality |x|<4: -3, -2, -1, 0, 1, 2, and 3.

Step-by-step explanation:

The question asks how many integers satisfy the inequality |x|<4. This means we are looking for all the integer values of x that when taken as absolute values are less than 4. To find the integers that satisfy this condition, we observe that the inequality holds for all integers between -3 and 3 inclusive, because the absolute value of any of those numbers is less than 4. Therefore, the integers that satisfy the inequality are -3, -2, -1, 0, 1, 2, and 3.

Total, there are seven integers that satisfy the inequality |x|<4. Remember, zero is included in this count since the absolute value of zero is 0, which is less than 4.

Answer 2

Infinite number of integers that satisfy the inequality |x|<4.

Step-by-step explanation:

The absolute value of a number indicates its distance from 0 on the number line. Therefore, the inequality |x|<4 indicates that x is less than 4 units away from 0 on the number line. Because there are an infinite number of integers on the number line, there are an infinite number of integers that satisfy the inequality |x|<4.