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) About Me  (Show Source):
You can put this solution on YOUR website!
2%3C3x%3C9 Start with the given compound inequality.


%282%29%2F3%3Cx%3C%289%29%2F3 Divide all sides by 3.


2%2F3%3Cx%3C3 Reduce.


So our answer is 2%2F3%3Cx%3C3



Here's the graph of the solution set

Graph of the solution set

Note:
There is an open circle at x=2%2F3 which means that we're excluding this value from the solution set
Also, there is an open circle at x=3 which means that we're excluding this value from the solution set.

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
2%3C3x%3C9. First take each part of the inequality separately. Let's start with 3x%3C9. Divide by three and get x%3C3 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

graph%28+500%2C+500%2C+3-5%2C+3%2B5%2C+-10%2C+10%2C+1000000x-1000000%2A3+%29+


Now deal with the other side 2%3C3x. Divide both sides by three and get 2%2F3%3Cx or x%3E2%2F3. 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 2%3C3x%3C9.
If you still need help: http://www.algebra.com/algebra/homework/Graphs/Inequalities-Made-Easy.lesson