Question

Write an absolute value inequality for which the interval shown is the solution.

A) ∣x−3∣<4

B) ∣x−3∣>4

C) ∣x+3∣<4

D) ∣x+3∣>4

Answer 1

To find the absolute value inequality that represents the given interval, we analyze the given options. Option C, ∣x+3∣<4, is the correct answer.

Step-by-step explanation:

To write an absolute value inequality for which the interval shown is the solution, we need to analyze the inequality options and determine which one satisfies the given interval. The given interval is (3-4, 3+4), which represents the range from 3-4 to 3+4. Let's analyze the options:

A) ∣x−3∣<4: This means the distance between x and 3 is less than 4. However, the given interval extends beyond 4, so this option does not satisfy the given interval.

B) ∣x−3∣>4: This means the distance between x and 3 is greater than 4. Since the given interval extends up to 4, this option also does not satisfy the given interval.

C) ∣x+3∣<4: This means the distance between x and -3 is less than 4. This option satisfies the given interval, as the distance from 3 to -3 is within 4.

D) ∣x+3∣>4: This means the distance between x and -3 is greater than 4. Since the given interval extends up to 4, this option does not satisfy the given interval.

Therefore, the correct answer is option C) ∣x+3∣<4.