SOLUTION: solve each compound ineqaulity and write the solution set using interval notation. -3<(3x-1)/5<1/2 and 1/3<(3-2x)/6<9/2

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Question 30617: solve each compound ineqaulity and write the solution set using interval notation.
-3<(3x-1)/5<1/2 and 1/3<(3-2x)/6<9/2
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+-3%3C%283x-1%29%2F5%3C1%2F2+ and +1%2F3%3C%283-2x%29%2F6%3C9%2F2+
We will solve these one at a time. As these are compound inequalities, like an equation where if you add 5 to each side .... here you do it to all three parts of the inequality.
+-3%3C%283x-1%29%2F5%3C1%2F2+ Multiply by 5
+-15%3C3x-1%3C5%2F2+ Add 1
+-14%3C3x%3C7%2F2+ divide by 3
+-14%2F3%3Cx%3C7%2F6+ the smaller value is on the left, the larger on the right, and the <> symbols are pointing left. If you need to reduce the fractions to mixed numbers, do so now.
+1%2F3%3C%283-2x%29%2F6%3C9%2F2+ Multiply by 6
+6%2F3%3C3-2x%3C54%2F2+ reduce the fractions now
+2%3C3-2x%3C27+ subtract 3
+-1%3C-2x%3C24+ Divide by negative 2
DONT FORGET TO FLIP THE < > SYMBOL WHEN * OR / BY A NEGATIVE!!!!
+1%2F2%3Ex%3E-12+ Smaller number needs to be on the left ... flip the WHOLE thing end for end
+-12%3Cx%3C1%2F2+