Question

Tavon says that for the absolute value inequality |z| < 6, you read the inequality as 'z is less than 6 away from zero.' Marta believes you read the inequality as 'z is less than 6.' Who is correct? Explain.

Answer 1

Tavon is correct.

Explanation:

|z| is the absolute value of z, which means the distance from 0 on the number line without considering the direction, which will be always a positive number or zero.

Marta says 'z is less than 6'. This is only valid until z is greater than -6, because if for example z is -7:

|-7| < 6

7 < 6 this is not true

On the other hand Tavon is saying the definition of absolute value in their statement.