SOLUTION: Find the solution set. |2x-2| is < or = to 2

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Question 33565: Find the solution set.
|2x-2| is < or = to 2

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
y = |2x-2| means 2 straight lines: 2x-2 and -(2x-2). They form a V-shaped graph, as shown:

+graph%28300%2C300%2C+-4%2C+6%2C+-2%2C+10%2C+abs%282x-2%29%29+

The question is asking "for what values of x is this graph less than or equal to y=2. Lets look at both these graphs:

+graph%28300%2C300%2C+-4%2C+6%2C+-2%2C+10%2C+abs%282x-2%29%2C+2%29+

Looking at the graph, the V-shape is less than or equal to the y=2 horizontal line between x=0 and x=2. These are the answers. Lets now try to get these 2 answers through algebra:

+2x-2+%3C=+2+
+2x+%3C=+4+
+x+%3C=+4%2F2+
+x+%3C=+2+

and +-%282x-2%29+%3C=+2+
+2x-2+%3E=+-2+ note the < has changed to a >
+2x+%3E=+0+
+x+%3E=+0+

So, +x+%3E=+0+ and +x+%3C=+2+
or +0+%3C=+x+%3C=+2+ which matches the findings from the graph

jon.