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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Sep 711:06 PM
Solving Linear
& Graphing
Inequalities
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Sep 131:02 PM
Open circle on the graph means that the
inequality will be greater than or less than.
Closed circle on the graph means that the
inequality will be “greater than or equal to”
OR “less equal than or equal”.
> or
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Sep 131:08 PM
If the direction of the GRAPH is pointed to the LEFT, then inequality is "less than" or "less than or equal to".
If the direction of the GRAPH is pointed to the RIGHT, then inequality is "greater than" or "greater than or equal to".
10 2 3 4 5 6 7 8 9 1012345678910
10 2 3 4 5 6 7 8 9 1012345678910
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 2111:03 AM
>greater thanside of any inequality less thanside of any inequality>greater than
side of any inequality
less thanside of any inequality
OR
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Sep 1312:58 PM
EXAMPLE 1
Given the graph, below :
012345 1 2 3 4 5 6 767
orb)
SOLUTION
b) Write an inequality to express the graph on the number line, use x as your variable.
a) Write a statement in words to express the graph on the number.
a) All numbers less than 2.–
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Sep 131:23 PM
EXAMPLE 2
012345 1 2 3 4 5 6 767
SOLUTION
orb)
Given the graph, below :
b) Write an inequality to express the graph on the number line, use x as your variable.
a) Write a statement in words to express the graph on the number.
a) All numbers greater than or equal to 5.–
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 2111:13 AM
SOLUTION
Solve the inequality, then graph the solution set on a number line.
EXAMPLE 3
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 2111:20 AM
012345 1 2 3 4 5 6 767
+ 7 + 7
6 6
x 3x is greater than or equal to 3
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 2111:25 AM
EXAMPLE 4
Solve the inequality, then graph the solution set on a number line.
SOLUTION
23
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 2111:30 AM
23
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 2111:37 AM
EXAMPLE 5
Solve the inequality, then graph the solution set on a number line.
SOLUTION
Eliminate the fractions by multiplying the entire equation by the least common denominator.
Least common denominator of 4, 14, and 7 is 28.
28( )
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 2111:41 AM
28( )
28 28 28– –
28 28 28– – 7 2 4
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 2112:01 PM
+ 4x4x+
+21 +21
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 2112:03 PM
Keep the direction of the inequality symbol the same, we divided by a positive number. It does matter that the solution is negative number.
012345 1 2 3 4 5 6 767
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 211:28 PM
EXAMPLE 6
Solve the inequality, then graph the solution set on a number line.
SOLUTION
1
+ x + x
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Sep 710:14 PM
The inequality is TRUE.
ALL REAL NUMBERS
012345 1 2 3 4 5 6 767
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 211:35 PM
EXAMPLE 7
Solve the inequality, then graph the solution set on a number line.
SOLUTION
– 6x – 6x
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 211:39 PM
The inequality is FALSE.
012345 1 2 3 4 5 6 767
NO SOLUTION
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Sep 1312:44 PM
COMPOUND
INEQUALITIES
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 211:42 PM
EXAMPLE 8
Solve the inequality, then graph the solution set on a number line.
SOLUTION
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 211:44 PM
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Sep 710:33 PM
AND
How to graph a compound inequality ?
Rewrite as 2 separate inequalities.
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 211:40 PM
012345 1 2 3 4 5 6 767
Graph each inequality separately.
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Sep 132:08 PM
012345 1 2 3 4 5 6 767
012345 1 2 3 4 5 6 767
When graphing compound inequalities with an AND, we will take the INTERSECTION of the graphs.
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 212:18 PM
EXAMPLE 9
Solve the inequality, then graph the solution set on a number line.
SOLUTION
4x + 3 6x >11– OR – –4 (3x 5) 12
4x + 3 6x >11– OR – –4 1(3x 5) 12
2x + 3
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Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook
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October 25, 2017
Oct 211:55 PM
2x 8– 2– 2– >
OR –9 3x 12
– 3x 3x
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