SOLUTION: How to solve out 3/5t-1/10t=t-5/2

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Question 213471This question is from textbook Introductory and Intermediate Algebra
: How to solve out 3/5t-1/10t=t-5/2 This question is from textbook Introductory and Intermediate Algebra

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
3t%2F5-t%2F10=t-5%2F2

The following steps will solve the above equation

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


YOUR ANSWER


  • This is an equation! Solutions: t=5.
  • Graphical form: Equation 3t%2F5-t%2F10=t-5%2F2 was fully solved.
  • Text form: 3t/5-t/10=t-5/2 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3t%2F5-t%2F10=t-5%2F2+%29
    For tutors: simplify_cartoon( 3t/5-t/10=t-5/2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+3%2At%2F5+%29-highlight_red%28+t%2F10+%29=t-5%2F2.
Eliminated similar terms highlight_red%28+3%2At%2F5+%29,highlight_red%28+-t%2F10+%29 replacing them with highlight_green%28+%283%2A1%2F5-1%2F10%29%2At+%29
It becomes highlight_green%28+%283%2A1%2F5-1%2F10%29%2At+%29=t-5%2F2.
Look at %28highlight_red%28+3+%29%2Ahighlight_red%28+1+%29%2F5-1%2F10%29%2At=t-5%2F2.
Multiplied numerator integers
It becomes %28highlight_green%28+3+%29%2F5-1%2F10%29%2At=t-5%2F2.
Look at %28highlight_red%28+3%2F5+%29-highlight_red%28+1%2F10+%29%29%2At=t-5%2F2.
Added fractions or integers together
It becomes %28highlight_green%28+5%2F10+%29%29%2At=t-5%2F2.
Look at highlight_red%28+%28highlight_red%28+5%2F10+%29%29%2At+%29=t-5%2F2.
Remove unneeded parentheses around factor highlight_red%28+5+%29,highlight_red%28+1%2F10+%29
It becomes highlight_green%28+5+%29%2Fhighlight_green%28+10+%29%2At=t-5%2F2.
Look at highlight_red%28+5+%29%2Fhighlight_red%28+10+%29%2At=t-5%2F2.
Factors 5 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes highlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2At=t-5%2F2.
Look at highlight_red%28+1+%29%2F2%2At=t-5%2F2.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes t%2F2=t-5%2F2.
Look at t%2F2=highlight_red%28+t-5%2F2+%29.
Moved these terms to the left highlight_green%28+-t+%29,highlight_green%28+5%2F2+%29
It becomes t%2F2-highlight_green%28+t+%29%2Bhighlight_green%28+5%2F2+%29=0.
Look at highlight_red%28+t%2F2+%29-highlight_red%28+t+%29%2B5%2F2=0.
Eliminated similar terms highlight_red%28+t%2F2+%29,highlight_red%28+-t+%29 replacing them with highlight_green%28+%281%2F2-1%29%2At+%29
It becomes highlight_green%28+%281%2F2-1%29%2At+%29%2B5%2F2=0.
Look at %28highlight_red%28+1%2F2+%29-highlight_red%28+1+%29%29%2At%2B5%2F2=0.
Added fractions or integers together
It becomes %28-highlight_green%28+1%2F2+%29%29%2At%2B5%2F2=0.
Look at highlight_red%28+%28-highlight_red%28+1%2F2+%29%29%2At+%29%2B5%2F2=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F2+%29
It becomes -highlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2At%2B5%2F2=0.
Look at -highlight_red%28+1+%29%2F2%2At%2B5%2F2=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -t%2F2%2B5%2F2=0.
Look at highlight_red%28+-t%2F2%2B5%2F2+%29=0.
Solved linear equation highlight_red%28+-t%2F2%2B5%2F2=0+%29 equivalent to -0.5*t+2.5 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: t=5.

Universal Simplifier and Solver


Done!



I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J