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Chapter 4
Inequalities
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4.1 Inequalities and Their Graphs
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An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs:
≤
A ≤ B
A is less than or
equal to B.
<
A < B
A is lessthan B.
>
A > B
A is greaterthan B.
.
≥
A ≥ B
A is greaterthan or
equal to B.
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Ex 1: Determine whether the given number is a solution of the inequality of
x >4a.) 4
4>4
False
b.) 0
0>4
False
c.) -4
-4>4
False
d.) 6
6>4
True
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3. Draw your solution graph line in the same direction as the inequality IF the “x” is on left.
Graph the Inequality on the # line
1. Draw number line. Label zero and the number where your arrow starts
2. Put a circle on the number.
Open Circle if < or >.
Solid Circle if “or equal to” ≤or≥.
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Ex 2: Graph the solution ofx > -2
-2-6 -4 0 642
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Ex 3: Graph the solution of
x -2If you have ≤ or ≥ you draw a closed circle
-2-6 -4 0 642
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Hint: When graphing make sure your variable is on the left side
5 < x
To make sure the graph is correct switch the variable and number and flip the inequality.
x>5
Now graph it
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Ex 4: This is the graph of:
1) x -2
2) x > -2
3) x -2
4) x < -2
-2-6 -4 0 642
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Ex 5: This is the graph of:
1) x 1
2) x > -1
3) x -1
4) x > 1
-2-6 -4 0 642
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4.2
The Addition Property of Inequalities
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Addition Property of InequalitiesIf a < b, then
a + c < b + c
The same is true for >, , and
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Ex 6: Solve for “x”and graph:x - 3 > 4
+3 +3
X > 7
-4 -8 0 84
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Ex 7: Solve for “x” and graph:
8z + 6 – 7z 16
Z + 6 16-6
z 10
-4 -8 0 84
-6
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Ex 8: Solve: 1 1
3 4x
4 3
12 12x
3 4
12 12x
7
12x
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Ex 9: 5(y-2)-4(y-1)<0
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Assignment:Page 173 (4-18, 26-30) even
Page 178 (8-36) even