Chapter 6
Solving Linear
Inequalities
Note Packet
Name:
Teacher:
Period:
6-1 Solving Linear Inequalities by Addition & Subtraction
Example # 1 Solve: s - 12 > 65
** Remember: We use ◦ for < or > , and ● for ≤ or ≥. **
Example # 2 Solve, then graph the solution on a number line.
12 ≥ y - 9
Example # 3 Solve, then graph the solution on a number line.
q + 23 ≤ 14
Example # 4
Solve, then graph the solution on a number line.
12n - 4 < 13n
Homework Pg 321 # 14-36 even
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6-2 Solving Inequalities by Multiplication & Division
Example # 1: Solve
Date:
g
< 12
3
** Remember: If you multiply or divide by a negative number, you MUST change the direction
of the inequality symbol. **
Example # 2: Solve
3
d ≥ 6
4
Example # 3: Write an inequality for the sentence below, then solve.
Four-fifths of a number is at most twenty.
Example # 4: Solve
12f ≥ 60
Example # 5:
-8p < 136
Solve
Homework Pg 329 # 13-18 all, 20-34 even
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6-3 Solving Multi-Step Inequalities
Example # 2:
Solve
Example # 3:
Write an inequality for the sentence below, then solve.
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Date:
13-11d ≥ 79
Four times a number plus twelve is less than a number minus 3.
Example # 4:
Solve
8- (c+3) ≤ 6c + 3(2-c)
Example # 5: Solve -7(x + 4) + 11x ≥ 8x - 2(2x + 1)
Homework Pg 335 # 16-30 even, 36, 38
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6-4 Solving Compound Inequalities
Date:
Example # 1. Graph the solution set of y ≥ 5 and y < 12.
AND: Both are true at
the same time.
Example # 2
Solve, then graph.
7 < z + 2 ≤ 11
Example # 3 A ski resort has several types of hotel rooms and several types of cabins. The
hotel rooms cost at most $89 per night, and the cabins cost at least $109 per
night. Write and graph a compound inequality that describes the amount a guest
would pay per night at the resort.
OR: Either one is true.
Example # 4:
Solve and graph
4k - 7 ≤ 25 or 12 - 9k ≥ 30
Example: Write a compound inequality for each graph below.
a.
b.
4
10
Homework Pg 342 # 14 - 44 even
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6-5 Solve Open Sentences Involving Absolute Value.
Date:
Absolute value:
Example:
Graph
Example # 1: Solve
a. x
=4
b4
=5
b. x
< 4
c. x
>4
Example # 2: Write an absolute value inequality for the given graph.
l x - middle l = distance from
3 4 5 6 7 8 9
Example # 3: Solve then graph.
y  3 ≤ 12
Example # 4: Solve then graph.
3y  3 > 9
Homework Pg 349 # 14-19 all, 24-34 even
the middle
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6-6 Graphing Inequalities in Two variables
Date:
Remember: When we graph a line we use slope-intercept form. (y = mx + b)
Example: Graph. y=
1
x+5
2
Example # 1: From the set {(3,3), (0,2), (2,4), (1,0)}, which ordered pairs are part of the
solution set for 4x + 2y > 8 ?
Remember: When we graph in 2 variables we change the
to
for < and >
and
to
for ≤ and ≥.
Example # 2: Graph 2y - 4x > 6
Example: Graph
y ≤
1
x -2
2
Homework Pg 356 # 12, 14, 20-23 all, 26-36 even
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