Question

Given the inequality -8 < 2, explain what happens when you multiply or divide both sides by 2 and what happens when you multiply or divide both sides by -2.

Answer 1

see explanation

Explanation:

Given

- 8 < 2 ← a True statement, then multiplying both sides by 2 gives

- 16 < 4 ← still a True statement, however, multiplying both sides by - 2 gives

16 < - 4 ← a False statement

However, if we reverse the inequality sign then

16 > - 4 ← is now a True statement

In conclusion

When multiplying or dividing by a positive quantity the sign remains the same.

When multiplying or dividing by a negative quantity the sign must be reversed.