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Math
A |
Solving
Linear Inequalities |
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Solving
linear inequalities is pretty much the same as solving linear
equations... |
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with
one very
important
exception.
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Look
at this true statement:
Suppose we multiply both sides by -1. |
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5
> 3
(-1)(5) ? (3)(-1)
-5 ? -3 |
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What
is the relationship between these two numbers ?
ANS:
-5 is
less
than
-3 because it is further to the left on the number line. |
-5
< -3
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So
we just learned the one exception. That is:
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When
you multiply
an inequality by a negative
number, it changes the direction of the inequality.
This is also
true if you divide
by a negative. |
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You
will want to remember what each inequality symbol means.
This will be easier to do if you remember that the open part of
the symbol always faces the larger quantity. |
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SYMBOL |
MEANING |
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less
than |
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greater
than |
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less
than or equal to |
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greater
than or equal to |
Solve
and graph the solution set of: 2x - 6 < 2
Add
6 to both sides.
Divide both sides by 2.
Open
circle at 4, since x can not equal 4, and an arrow to the left,
because we want values less
than 4. |
2x
- 6 < 2
2x < 8
x < 4
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Solve
and graph the solution set of: 5 - 3x 
13 + x
Solve
and graph the solution set of: 3(2x+4) > 4x+10
Multiply
out the parentheses.
Subtract 4x from both sides.
Subtract 12 from both sides.
Divide both sides by 2, but don't
change the direction of the inequality, since we didn't
divide by a negative.
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3(2x+4)
> 4x+10
6x+12 > 4x+10
2x+12 > 10
2x > -2
x > -1 |
| Open
circle
at -1, since x can not equal -1, and an arrow to the right,
because we want values larger
than -1. |
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How to use
your
TI-83+ graphing calculator with
linear inequalities.
Click calculator. |
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13
+ x
-2
