Question

Which of the following inequalities states that the distance between x and −2 is less than 7?

a) ∣x−(−2)∣<7
b) x+2<7
c) x−(−2)>7
d) ∣x+2∣<7

Answer 1

The correct inequality that states that the distance between x and -2 is less than 7 is option a) ∣x−(−2)∣<7.

Step-by-step explanation:

The correct inequality that states that the distance between x and -2 is less than 7 is option a) ∣x−(−2)∣<7.

To explain, the absolute value of x minus -2 should be less than 7. This means that the distance between x and -2 on a number line should be less than 7.

For example, if we choose x = -4, then the absolute value of (-4 - (-2)) is equal to 2, which is less than 7. Therefore, option a) satisfies the given inequality.