Transcript Warm Up – 9/1 or 9/2 Write your name and date

Warm-Up
Solve the linear inequality.
1. 2(x+4) > x + 3
Answers:
1. x > -5
2. x > 1
2. -5x+7 ≤ 4x – 2
Homework: WS 1.7B Pg. 175
(63-85 odds)
Homework Answers:
HW: Pg. 175 (1-15 odd, 27-39odds)
Announcements:
Ch #1 TEST – 100 point on 9/15 & 18!
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Sept 11!!!!!!!! THANK YOU
Objective:
To be able to use interval notation when solving linear
inequalities, recognize inequalities with no solution or
all real numbers as a solution, solve compound
inequalities and solve absolute value inequalities.
Lesson 1.7B
Solving a Compound Inequality
The solution
consists
all real
numbers
greater
Example
1: set
Solve
and of
graph
the
solution
set. than -2
less
1, represented
by side
-3<and
2x +1
≤ 3than or equal toSubtract
1 from each
{ x< -2<
notation
andsides
(-2,1]
-4
2x ≤x2≤ 1} in set-builder Divide
both
byin2 interval
notation.
(
]
-2 < x ≤ 1
Simplify
The graph is:
(
-2
]
0
1
You Try:
Solve and graph the solution set.
1 ≤ 2x + 3 < 11
Answer:
[-1, 4)
[
-1
)
4
Solving Inequalities with
Absolute Value
Rules to follow:
If X c then –c < X <c.
If
X c
then X < -c or X > c.
These rules are valid if < is replaced with ≤ and >
is replaced with ≥.
Example 2:
Solve and graph the solution set.
x  4 3
Given
-3 < x-4 <3
Follow rule because of < sign
1<x<7
Add four to both sides
The solution set is (1,7).
(
)
1
7
You Try:
Solve and graph the solution set.
*******Remember to isolate the absolute
value sign first.
 2 3x  5  7  13
Answer:
-5≤x ≤ 5/3, [ -5, 5/3]
[
]
-5
0
1 2
Example 3:
7 5  2 x
Given
Switch equation around
5  2x 7
Rewrite following rule
5  2 x7or 5  2 x 7
Solve
 2 x12or  2 x 2
Remember when dividing
x 6 or
x 1
by a negative to switch
the signs
1
)
6
(
The solution set is (-∞, -1)
OR (6,∞)
You Try!!
18 6  3x
Answer:
(-∞, -4) OR (8, ∞)
Graph
)
-4
(
8
Summary: Describe how to solve an
absolute value equation involving the >
symbol.