Question 114832
{{{2x/3}}}-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:
{{{2x/3}}}-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(6)/3}}}-2 =? 8-6
{{{12/3}}}-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(0)/3}}}-2 ≤? 8-0
{{{0/3}}}-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.