Question

Which inequalities are equivalent to n + 15 less-than 22? Select three options.
n + 15 minus 15 less-than 22 minus 15
n + 15 less-than 22 minus 15
n + 15 minus 22 less-than 22 minus 22
n + 15 + 6 less-than 22 + 6
n + 15 minus 22 less-than 22

Answer 1

The equivalent inequalities are:
- n + 15 − 15 < 22 − 15 (gives n < 7)
- n + 15 − 22 < 22 − 22 (gives n − 7 < 0 → n < 7)
- n + 15 + 6 < 22 + 6 (gives n + 21 < 28 → n < 7)

Each adds or subtracts the same number on both sides, so they are equivalent. The others change only one side and are not equivalent.