Question

Which values satisfy the inequality? |z| ≤ 5

Choose all answers that are correct.







A.

z = –6






B.

z = –5






C.

z = –1






D.

z = 8

Answer 1

|z| ≤ 5 ⇔ z ≤ 5 ∧ z ≥ -5 ⇒ -5 ≤ z ≤ 5

Answer:
B. -5 because -5 ≤ -5 ≤ 5
C. -1 because -5 ≤ -1 ≤ 5

Answer 2

B and C

When finding the absolute value of a number, a simple way to think of it is taking away a negative sign if there is one.

After making every number positive we can see that 5 and 1 are less than or equal to 5.