SOLUTION: solve each inequality. write solution in interval notation x/5-x/4 < 1 -

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Question 917992: solve each inequality. write solution in interval notation
x/5-x/4 < 1
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Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %28x%2F5%29-%28x%2F4%29%3C1 simplifies to -x%2F20%3C1
  • Text form: (x/5)-(x/4)<1 simplifies to -x/20<1
  • Cartoon (animation) form: simplify_cartoon%28+%28x%2F5%29-%28x%2F4%29%3C1+%29
    For tutors: simplify_cartoon( (x/5)-(x/4)<1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28x%2F5%29+%29-%28x%2F4%29%3C1.
Remove unneeded parentheses around terms highlight_red%28+x%2F5+%29
It becomes highlight_green%28+x%2F5+%29-%28x%2F4%29%3C1.
Look at x%2F5-highlight_red%28+%28x%2F4%29+%29%3C1.
Remove unneeded parentheses around terms highlight_red%28+-x%2F4+%29
It becomes x%2F5-highlight_green%28+x%2F4+%29%3C1.
Look at highlight_red%28+x%2F5+%29-highlight_red%28+x%2F4+%29%3C1.
Eliminated similar terms highlight_red%28+x%2F5+%29,highlight_red%28+-x%2F4+%29 replacing them with highlight_green%28+%281%2F5-1%2F4%29%2Ax+%29
It becomes highlight_green%28+%281%2F5-1%2F4%29%2Ax+%29%3C1.
Look at %28highlight_red%28+1%2F5+%29-highlight_red%28+1%2F4+%29%29%2Ax%3C1.
Added fractions or integers together
It becomes %28-highlight_green%28+1%2F20+%29%29%2Ax%3C1.
Look at highlight_red%28+%28-highlight_red%28+1%2F20+%29%29%2Ax+%29%3C1.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F20+%29
It becomes -highlight_green%28+1+%29%2Fhighlight_green%28+20+%29%2Ax%3C1.
Look at -highlight_red%28+1+%29%2F20%2Ax%3C1.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -x%2F20%3C1.
Result: -x%2F20%3C1

Universal Simplifier and Solver


Done!


hence -x/20 <1
multiply with -1 on both sides
-1* -x/20 <-1*1
x/20>-1
x>-20
solution is x is any number more than -20
x = (-20 ,infinity)