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Beginning Algebra
Tutorial 18: Solving Linear Inequalities

 Graph: *Inv. of add 3 is sub. 3   *Inv. of mult. by -2 is div. both sides by -2, so reverse inequality sign       *Visual showing all numbers less than -2 on the number line

 Notice how our variable was on the right side of the inequality.  It doesn't matter what side you have the variable on, as long as it by itself on one side and everything else is on the other side.  What you do have to be careful about is graphing it properly.  It is almost like reading it backwards this way.  So, if you feel more comfortable writing it with your variable on the left side, by all means, go ahead and do that.  Graph:  Since we needed to indicate all values less than -2, the part of the number line that was to the left of -2 was darkened. Since we are not including where it is equal to, an open hole was used. (return to problem 1a)

 Graph: *Distributive property   *Get x terms on one side, constants on the other side *Inv. of mult. by 2 is div. both sides by 2           *Visual showing all numbers less than or equal to 4 on the number line

 Graph:  Since we needed to indicate all values less than or equal to 4, the part of the number line that was to the left of 4 was darkened. Since we are including where it is equal to, a closed hole was used. (return to problem 1b)