Transcript Lesson 2-4: Solving Inequalities

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.
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
Open
circle
Closed
circle
Closed
circle
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]
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
Steps to Solve and Graph
1) Solve inequality (hear the bell when needed)
2) Make number line to include solution (usually 3 to 4 numbers is all you need)
3) Put circle on solution then decide if open or closed
4) Read inequality to decide which way to shade
(less than letter left: greater than letter right)
5) Check solution
Example 2
Graph y < -2
-3
-2
-1
Do not write steps
• Done
2) 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
• Example 3
Graph 5 > x
4
5
6
Do not need to write all steps
•
Done
2) 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
Example 4: Solve and Graph
1)
17  5 y  8 y  5
 13 y  22
22
y
13
Move variables to left constants to right
Hear the bell?
0
1
2
3
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 22 so shade to right
13
22
5) Pick a point line goes through see if it is true 10 > 13
What is the solution in interval notation?
so yes
[
22
,
13
∞)
Marker Boards pg 77-78
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38
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Assignment
2-4 /77 /1-39 eoo,
(on 9-39 solve, interval notation and graph)