Question 1208858
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There are at least two methods we can use to solve.


Method 1


0 < 1 - (x/3) < 1
0-1 < 1 - (x/3)-1 < 1-1 ........ see note1
-1 < -x/3 < 0
-1*(-3) > -3*(-x/3) > -3*0 ........ see note2
3 > x > 0
<font color=red>0 < x < 3</font>


Notes:<ol><li>Subtract 1 from all sides</li><li>Multiply all sides by -3. Multiplying all sides by a negative number will flip the inequality sign.</li></ol>Anyways, we conclude the solution is <font color=red>0 < x < 3</font>


The interval notation would be (0,3)
Be sure not to mix this up with ordered pair notation.


The graph on a number line will have open holes at 0 and 3; with shading in between.
In words: x is any number between 0 and 3 excluding each endpoint.


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Method 2


a < b < c is the same as saying a < b and b < c


0 < 1 - (x/3) < 1 breaks down into 0 < 1 - (x/3)  and  1 - (x/3) < 1 


Let's solve the first part.
0 < 1 - (x/3)
x/3 < 1
x < 3


Now solve the second part.
1 - (x/3) < 1 
-x/3 < 0
x > 0 .... see note2 mentioned earlier


We conclude that x > 0 and x < 3
Put another way:  0 < x and x < 3
Those collapse or glue together to get <font color=red>0 < x < 3</font> 
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