SOLUTION: Hello, I have not taken math in 3 years and started calculus this semester but have forgotten everything! Can you please help me solve this question please.. Find all real numbe

Algebra ->  Inequalities -> SOLUTION: Hello, I have not taken math in 3 years and started calculus this semester but have forgotten everything! Can you please help me solve this question please.. Find all real numbe      Log On


   

Question 703282: Hello, I have not taken math in 3 years and started calculus this semester but have forgotten everything! Can you please help me solve this question please..
Find all real numbers satisfying the inequality +%281%2F5%29x-x%3C16+
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%281%2F5%29x-x%3C16+
+x%2A%28+1%2F5+-+1+%29+%3C+16+
+%28-4%2F5%29%2Ax+%3C+16+
I need to multiply both sides by +-5%2F4+ to
get +x+ alone on the left side. Whenever you
multiply both sides by a negative number, the
sense of the inequality sign has to reverse, so
+x+%3E+%28-5%2F4%29%2A16+
+x+%3E+-20+
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I can check by saying +x+=+-20+ which should fail
the inequality.
+%281%2F5%29x-x%3C16+
+%281%2F5%29%2A%28-20%29+-+%28-20%29+%3C+16+
+-4+%2B+20+%3C+16+
+16+%3C+16+ fails, as it should
---------------
Now I try +x+=+-19+, which is greater than +-20+
+%281%2F5%29x-x%3C16+
+%281%2F5%29%2A%28-19%29-%28-19%29%3C16+
+-19%2F5+%2B+19+%3C+16+
+-3.8+%2B+19+%3C+16+
+15.2+%3C+16+ passes
OK