SOLUTION: 2<3x<9 solve the solution and graph it

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Question 147567: 2<3x<9
solve the solution and graph it
Found 2 solutions by jim_thompson5910, mangopeeler07:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given compound inequality.


Divide all sides by 3.


Reduce.


So our answer is



Here's the graph of the solution set

Graph of the solution set

Note:
There is an open circle at which means that we're excluding this value from the solution set
Also, there is an open circle at which means that we're excluding this value from the solution set.
Answer by mangopeeler07(462)   (Show Source): You can put this solution on YOUR website!
. First take each part of the inequality separately. Let's start with . Divide by three and get To graph it, first do the graph of x=3.
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
this equation defines a vertical line.

  • X intercept: 3. X intercept is the intersection of the line with the x axis.

  • Y intercept: not defined (the line IS vertical)

  • Slope: not defined, can be thought of as infinite



Now deal with the other side . Divide both sides by three and get or . Now, draw the line for x=2/3 on the same graph as x=3.
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
this equation defines a vertical line.

  • X intercept: 0.666666666666667. X intercept is the intersection of the line with the x axis.

  • Y intercept: not defined (the line IS vertical)

  • Slope: not defined, can be thought of as infinite



Then simply erase parts of both lines to dot them to show that x does not include those values. Now shade the area between the lines. You are done graphing the inequality .
If you still need help: http://www.algebra.com/algebra/homework/Graphs/Inequalities-Made-Easy.lesson