Algebra 1 Inequalities
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The 4 Musketeers
Inequalities

 

 Sometimes we have equations that don't use an equal sign (=).

 They use one of 4 other squiggles.
 The contestants are:
 
 # 1

 

 This means "greater than".
 It means the stuff on the left side of the equation
 has a greater value than the stuff on the right side.
 Another way to think of inequalities, is that in all of these problems
 the inequality arrow always points towards the stuff with less value.
 As in:

 

 
 # 2

 

 This puppy means "less than".
 It means that the stuff on the left side of the equation
 has a lesser value than the stuff on the right side.
 As in:

 

 
 # 3

 

 This one means "greater than OR equal to".
 It is a combination of ">" and "=".
 It means that the stuff on the left side
 either has a greater value or is of equal value
 than the stuff on the right side.
 As in:

 
 # 4

 

 The last of our musketeers.
 This one means "less than OR equal to".
 It is a combination of "<" and "=".
 It means that the stuff on the left side
 either has a lesser value or is of equal value
 than the stuff on the right side.
 As in:

 
 When you get an equation with one of these things in it,
 it makes NO DIFFERENCE in how you work the problem.
 Just use the same two rules in the same way.
 
 There is ONE EXTRA DETAIL
 that you need in some of these problems.
 
 If you multiply or divide both sides by a negative number,
 you reverse the direction that the inequality arrow points.
 
 OK, now we're ready to try some problems!
 
 Example:

5X - 3 > 2

 
 First you add 3 to both sides ...
 

 
 Now divide both sides by 5
 to get the X all by itself.
 

 
 And simplify ...

X > 1

 
 OK, now in this next example,
 we will need that "reverse the direction" trick.
 
 Solve this for X ...

 

 
 First peel the "+ 1" away from the X.
 

 

 
 Now divide by -3 and watch the inequalities
 change direction ...
 

 

 

   copyright 2005 Bruce Kirkpatrick

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