SOLUTION: 5-2x|≤4 5-2x≤4......or.....5-2x≥-4 -2x≤-1..............-2x≥-9 x≥1/2................x≤9/2 I understand that what I don't under

Algebra ->  Inequalities -> SOLUTION: 5-2x|≤4 5-2x≤4......or.....5-2x≥-4 -2x≤-1..............-2x≥-9 x≥1/2................x≤9/2 I understand that what I don't under      Log On


   

Question 903850: 5-2x|≤4
5-2x≤4......or.....5-2x≥-4
-2x≤-1..............-2x≥-9
x≥1/2................x≤9/2

I understand that what I don't understand is how x≥1/2 or x≤9/2 can then be translated to mean 1/2≤x≤9/2....how do the signs change to be both in the same direction when they were both in opposite directions. Please help explain this to me.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
That "or" should be "and". This is because |x| < k turns into "x < k and x > k" for some positive number k.

You should end up with "x≥1/2 and x≤9/2" (again notice the "and")

Combining the two gives you 1/2≤x≤9/2

Side Note: x≥1/2 is the same as 1/2≤x. Everything is just flipped.