Question 114832: 2x/3 - 2 ≤ 8 - x
Answer by jgr45(31)   (Show Source):
You can put this solution on YOUR website!  -2 ≤ 8-x
First off, remember that inequalities are solved exactly the same way as equations. The only difference is when you multiply/divide by a negative number, the sign has to change to the opposite.
Start by multiplying each term by 3 to eliminate the fraction:
2x - 6 ≤ 24 - 3x
Now get the variables on one side and constants on the other:
2x ≤ 30 - 3x (adding 6)
5x ≤ 30 (adding 3x)
x ≤ 6
Check:
-2 =? 8-x
To check your answer, treat the expression as an equation, because we're only concerned with the boundary, or endpoint, of the graph. Subbing 6 for x:
 -2 =? 8-6
 -2 =? 2
4-2 =? 2
2 = 2, Check.
Now to check to see if the graph is going in the correct direction, often a good number to try is 0 (the origin). So--plug in 0 for x, and this time keep the original sign:
 -2 ≤? 8-0
 -2 ≤? 8
Please note that it is permissible for a dividend/numerator to be 0. It is the DIVISOR, or DENOMINATOR, that cannot be 0.
0-2 ≤? 8
-2 ≤ 8 -- A true statement, so 0 should be included in the solution and should be part of the graph. Therefore the arrow should be drawn in the direction from 6 that includes 0, namely the left side.
If you were asked to graph the solution, it would be a closed point at 6 and everything to the left.
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