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An inequality is a special
equation that describes how two expressions are not equal. The signs
<, ≤, ≠, >, and ≥ are used to express inequalities. The
equal sign is sometimes used but strictly speaking is not an inequality but is
an equality.
Examples:
2
< 3 (read: 2 is less than 3)
4 ≠ 5
(read: 4 is not equal to 5)
x ≤ 7
(read: x is less than or equal to 7)
In this last example, x
represents all numbers that are less than seven and seven itself,
but no numbers greater than 7.
x ≥ 7
(read: x is greater than or equal to 7)
In other words, x represents
all numbers greater than 7 and 7 itself, but no numbers less than 7.
The number line is useful for visualizing
inequalities. Lines are drawn on top of the number line with arrows to
show the range of the inequality. You will notice the start of the lines shown
with circles or filled in circles. The circle means that value is not
included, while the filled in circle means that value is included. The
following diagram illustrates how to use number lines to show inequalities.
Inequalities are “solved”
using the normal rules and steps
for solving linear equations. However, if you multiply (or
divide) by a negative number, then you must reverse the sense of the
inequality.
Examples:
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3x + 5 < 2x - 4
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-2x + 3x + 5 < 2x -4 -2x
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Isolate the unknown x
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x + 5 < -4
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-5 + x + 5 < -4 -5
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x < -9
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Answer
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Let's talk about negative numbers
used to multiply or divide inequalities.
Consider 3 < 5
Now if we multiply both sides by a
–1, we have –3 < –5, which we know
is
incorrect. So if we reverse the inequality sign < to > then we
have
–3
> –5, which is correct. (Review the number
line).
Example:
The following examples demonstrate how to graph inequalities.
This is another FREE Algebra PRINTABLE presented to you from the
Algebra section of
K12math.com
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