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Inequalities
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Equation Inequality
A statement that asserts the equality of 2 terms
A relationship between 2 terms that are of unequal value
Contains an equal sign = equal to
Contains an inequality sign< less than
> Greater than≤ less than or equal to
≥ greater than or equal to
Solution is one numberX + 5 = 10X = 5
Solution is more than one numberX + 5 < 10X < 5
Solution is represented by a single dot on the number line
Solution is represented by a solid or hollow dot and and arrow
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Inequalities
<Smaller value
Larger value
10 20
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Inequalities
<Larger value
Smaller value
20 10
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Inequalities<= ≥
Greater than
Equal to
Greater than or equal to
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Inequalities
<= ≤
Less than
Equal to
Less than or equal to
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Inequalities
≤xX is less than or equal to 5
5
5Solid Dot
All numbers
that are less
than or equal
to 5
Include 5 because x is less than or equal to 5
Line goes to the left because x is less than or equal to 5
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Inequalities
<xX is less than 5
5
5Hollow Dot
All numbers
that are less
than 5
Does not include 5 because x is only less than 5
Line goes to the left because x is less than 5
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Inequalities
≥xX is greater than or equal to 5
5
5
Solid Dot
All numbers that
are greater than
or equal to 5
Include 5 because x is greater than or equal to 5
Line goes to the right because x is greater than or equal to 5
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Inequalities
>xX is greater than 5
5
5
Hollow Dot
All numbers that
are greater than 5
Does not include 5 because x is only greater than 5
Line goes to the right because x is greater than 5
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Inequalities
-2 0 2 4 6-4-6
X ≥ 0
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Inequalities
-2 0 2 4 6-4-6
X > 4
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Inequalities
-2 0 2 4 6-4-6
X ≤ -2
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Inequalities
-2 0 2 4 6-4-6
X < 6
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Inequalities
-2 0 2 4 6-4-6
X > -6
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Inequalities6 > x
Rewrite inequalities so that the variable is on
the left
x 6<If you switch
sides, the
inequality sign
needs to be
flipped
6 is greater than x
x is less than 6
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Inequalities
10 > x
Rewrite with the variable on the left:
x < 10n ≤ -6
-5 < y
-6 ≥ n y > -5
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Inequalities
10 > x +5
Rewrite with the variable on the left:
x + 5 < 10
n - 6 ≤ -6
-5 < 5y -6
-6 ≥ n - 6 5y – 6 > -5
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Solving One Step Inequalitiesx + 7 < 4
- 7 -7
x < -3
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Solving One Step Inequalities-5 ≥ x +
8
- 8 -8
x ≤ -13
x + 8 ≤ -5
Rewrite so that x is on the left, be sure to flip inequality sign
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Solving One Step Inequalitiesx – 10 > -4 + 10 +10
x > 6
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Solving One Step Inequalities -1 < x – 10
+ 10 +10 x >
9
x – 10 > -1 Rewrite so that x is on the left, be sure to flip inequality sign
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Solving One Step Inequalities 2x ≥ 10 2 2 x ≥ 5
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Solving One Step Inequalities -2x ≥ 10 -2 -2 x ≤ -5
When multiplying or dividing by a negative, the inequality sign must be flipped
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Solving Two Step Inequalities
3x + 7 ≥ 10 -7 -7
3x ≥ 3 3 3 x ≥ 1
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Solving Two Step Inequalities
-4x - 1 < 7 +1 +1
-4x < 8 -4 -4 x > -2
When multiplying or dividing by a negative, the inequality sign must be flipped
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Solving Two Step Inequalities
x + 5 > 11 2 -5 -
5x > 62
x > 12
x > 6 2
(2)
(2)
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Solving Two Step Inequalities x - 5 ≤ -2 -3
+5 +5 x ≤
3 -3
x ≥ -9
x ≤ 3 -3
When multiplying or dividing by a negative, the inequality sign must be flipped
(-3) (-3)
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Solving Two Step Inequalities -5 > 5x + 10
-10 -10 5x < -15
5 5 x < -3
5x + 10 < -5 Rewrite so that x is on the left, be sure to flip inequality sign