SOLUTION: solve the inequality 3-x≤x-4≤2x-9

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Question 1022158: solve the inequality
3-x≤x-4≤2x-9
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Trying to isolate x may be unworkable. Split into two inequalities and solve each.

3-x%3C=x-4
3-x-x%3C=x-4-x
3-2x%3C=-4
-2x%3C=-4-3
-2x%3C=-7
x%3E=7%2F2

AND

x-4%3C=2x-9
-4%3C=x-9
-4%2B9%3C=x
5%3C=x

These two separately say 7%2F2%3C=x and 5%3C=x. You might want to check in the intervals
which these critical x values create to see which do and do not satisfy the ORIGINAL combined
inequality.

x%3C=7%2F2? Pick x at 3 to check.
3-x%3C=x-4%3C=2x-9
3-%283%29%3C=3-4%3C=2%283%29-9
0%3C=-1%3C=-3
Certainly FALSE, as would be expected.

7%2F2%3C=x%3C5? Pick 4.
3-4%3C=4-4%3C=2%2A4-9
-1%3C=0%3C=-1-----TRUE. Actually FALSE.

Last interval, x%3E=5?
Pick 5.
3-5%3C=5-4%3C=2%2A5-9
-2%3C=1%3C=1
TRUE ---- This interval works.

The solution for the combined inequality is highlight%28highlight_green%28cross%28x%3E=7%2F2%29%29%29.
No. Not correct.
Initial solution post had mistake in the work on the middle interval.
The correct solution is highlight%285%3C=x%29.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
solve the inequality
3-x≤x-4≤2x-9
Solutions: highlight_green%28x+%3E=+5%29    OR     x+%3E=+7%2F2 (ignore as this is NOT a solution)