SOLUTION: Please help me solve this equation: 2-3x is less than 5(2-x) is less than or equal to 3(2-x)+10 Thank you.

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Question 855591: Please help me solve this equation:
2-3x is less than 5(2-x) is less than or equal to 3(2-x)+10

Thank you.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
First just translate the statement.

2-3x%3C5%282-x%29%3C=3%282-x%29%2B10

Do the multiplications.
2-3x%3C10-5x%3C=6-3x%2B10
2-3x%3C10-5x%3C=16-3x
A sensible step may be add 3x to each member, to result in:
2%3C10-2x%3C=16, which seems to be a very well chosen step.
coninue:
2-10%3C10-2x-10%3C=16-10
-8%3C-2x%3C=4
CAREFUL, DIVIDING BY NEGATIVE TWO,...
highlight%284%3Ex%3E=-2%29



Dividing by a negative value must reverse the direction of the inequality symbols.