Beginning Algebra Tutorial 18


Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 18: Solving Linear Inequalities


WTAMU > Virtual Math Lab > Beginning Algebra > Tutorial 18: Solving Linear Inequalities


 
 

checkAnswer/Discussion to 1a

 
ad1a1
 
 

Graph:
ad1a2


*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)
 


 

checkAnswer/Discussion to 1b

 
ad1b1
 
 

Graph:
ad1b2

*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)
 


 

checkAnswer/Discussion to 1c

 
ad1c1
 
 

Graph:
ad1c2
 
 

*Mult. both sides by the LCD
 

*Get x terms on one side, constants on the other
 
 
 
 

*Visual showing all numbers greater than or equal to 3 on the number line

 
 

Graph
Since we needed to indicate all values greater than or equal to 3, the part of the number line that was to the right of 3 was darkened.

Since we are including where it is equal to, a closed hole was used.

(return to problem 1c)
 

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WTAMU > Virtual Math Lab >Beginning Algebra >Tutorial 18: Solving Linear Inequalities


Last revised on July 27, 2011 by Kim Seward.
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