Table of Contents

Example 1 : Given −2x < 4 we want to solve for x. Divide both sides by −2 and
reverse the inequality. We get
and after cancelling we get
−2x
−2
> 4
−2
x > −2
Only do this when multiplying or dividing both sides of the inequality by a negative number.
Let’s see what happens when we don’t do this.
Example 2 : Observe that −1 < 2 is a true statement.
−1 < 2
−1
−1
<
2
−1
1 < −2
We have ended up with 1 < −2, which is a false statement.
Some examples of solving inequalities follow.
Example 3 :
Example 4 :
Example 5 :
x + 3 ≥ 4
x + 3 − 3 ≥ 4 − 3
x ≥ 1
x − 2 ≥ −5
x − 2 + 2 ≥ −5 + 2
x ≥ −3
5x ≥ 10
5
x
5
x
≥
≥
10
5
2
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