Section 2.6 Solving Inequalities
When you solve an inequality, the process you use is pretty much the same as for solving
an equation.
1. What you do to one side you must do to the other.
2. An inequality sign is used as opposed to an equal sign.
3. The inequality sign reverses direction if you multiply/divide by a negative number.
Let’s take a look at what the deal is behind item 3 above.
+ to both sides
- from both sides
Multiply by +
Divide by +
4 < 12
We know that is true.
4 + 2 < 12 + 2
6 < 14
Also true.
4 – 2 < 12 – 2
2 < 10
Still true.
4 * 5 < 12 * 5
20 < 60
Everything is still great.
4/2 < 12/2
2<6
Perfect.
Multiply by -
4 * (-6) < 12 * (-6)
-24 < -72
Oh, Oh. Not true.
Divide by -
4/(-1) < 12/(-1)
-4 < -12
Not good. False.
When multiplying or dividing by a negative value you MUST reverse the direction
of the inequality.
Solve for x.
4 x  5  35
4 x  40
Homework
Sample
x  10
There are different ways to express answers to solutions to inequalities. You will be
expected to use all successfully (graphing, interval notation, set builder notation). We
will review each in the following table.
1
2
3
4
5
6
7
8
1) 3  x  6
2) 3  x  6
3) 3  x  6
4) 3  x  6
5) x  6
6) x  6
7) x  3
8) x  3
Pick some problems from 1-98 (page 140).
Homework:
25-32
33-40
99
100
107
MLP (MyLabsPlus) and the following problems from the text.
Copy the problem and give all three answers. Use a ruler.
Do NOT copy the graph. Answer both questions.
Copy the inequalities. Answer the questions.
Copy the inequalities. Answer the questions.
Copy the problem. Solve.
MLP problems & Quiz are due ________ Text problems are due _________