1. Lesson 2-4: Solving Inequalities
Objective
Students will solve and graph inequalities using addition/subtraction/multiplication/division and check that a number is a solution.

2. < > ≤ ≥ Inequalities Words Is less than Is greater than
Is less than or equal to OR
at Most
Is greater than or equal to OR is at least
Symbols
On number line
<
Open circle
> ≤
Closed circle ≥

3. Interval Notation [ or ] Boundary number is included
( or ) Boundary number is not included
Write interval notation for the following:
x > 3
(3, ∞)
w ≤ -2
(- ∞,-2]

4. Solve inequalities like equations except…
If you multiply or divide an inequality by a negative, switch the inequality symbol.
Example 1
-9x > -8.1
You must switch the inequality!!! -9 -9
x < 0.9

5. Example 2 Graph y < -2 -3 -2 -1 Steps to Solve and Graph
Solve inequality (hear the bell when needed)
Make number line to include solution (usually 3 to 4 numbers is all you need)
Put circle on solution then decide if open or closed
Read inequality to decide which way to shade
(less than letter left: greater than letter right)
5) Check solution
Example 2
Graph y < -2
Do not write steps
Done
Solution in center 1 or 2 numbers on each side
3) -2 is boundary and equal so circle is closed
4) Read y is less than or equal to -2 so line is to left
5) Pick a point line goes through see if it is true -6 ≤ -2 so yes

6. Example 3 Graph 5 > x 4 5 6 Do not need to write all steps Done
Do not need to write all steps
Done
Solution in center 1 -2 numbers on each side
3) 5 is boundary and not equal so circle is open
4) Read 5 is greater than x so…. x is less than five so shade line to left
5) Pick a point line goes through see if it is true 5 > -1 so yes

7. Example 4: Solve and Graph1)
Move variables to left constants to right
Hear the bell?
2) Solution in center 1 -2 numbers on each side (between 1 and 2)
3) More than 1.5 and equal so circle is closed
4) Read y is greater than so shade to right
5) Pick a point line goes through see if it is true 10 > so yes
What is the solution in interval notation? [ , ∞)

8. Assignment
2-4 /77 /1-39 odd, 46-51
(on 8-39 solve and graph)