SOLUTION: Solve for a: a/22+2a-4.5=1+17a/11

Algebra ->  Equations -> SOLUTION: Solve for a: a/22+2a-4.5=1+17a/11      Log On


   

Question 38536: Solve for a:
a/22+2a-4.5=1+17a/11
Answer by lyra(94) About Me  (Show Source):
You can put this solution on YOUR website!
Here you go:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: a=11.
  • Graphical form: Equation %28a%2F22%29%2B%282a%29-%284.5%29=%281%29%2B%2817a%2F11%29 was fully solved.
  • Text form: (a/22)+(2a)-(4.5)=(1)+(17a/11) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%28a%2F22%29%2B%282a%29-%284.5%29=%281%29%2B%2817a%2F11%29+%29
    For tutors: simplify_cartoon( (a/22)+(2a)-(4.5)=(1)+(17a/11) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28a%2F22%29+%29%2B%282%2Aa%29-%284.5%29=%281%29%2B%2817a%2F11%29.
Remove unneeded parentheses around terms highlight_red%28+a%2F22+%29
It becomes highlight_green%28+a%2F22+%29%2B%282%2Aa%29-%284.5%29=%281%29%2B%2817a%2F11%29.
Look at a%2F22%2Bhighlight_red%28+%282%2Aa%29+%29-%284.5%29=%281%29%2B%2817a%2F11%29.
Remove unneeded parentheses around terms highlight_red%28+2%2Aa+%29
It becomes a%2F22%2Bhighlight_green%28+2%2Aa+%29-%284.5%29=%281%29%2B%2817a%2F11%29.
Look at a%2F22%2B2%2Aa-highlight_red%28+%284.5%29+%29=%281%29%2B%2817a%2F11%29.
Remove unneeded parentheses around terms highlight_red%28+-4.5+%29
It becomes a%2F22%2B2%2Aa-highlight_green%28+4.5+%29=%281%29%2B%2817a%2F11%29.
Look at highlight_red%28+a%2F22+%29%2Bhighlight_red%28+2%2Aa+%29-4.5=%281%29%2B%2817a%2F11%29.
Eliminated similar terms highlight_red%28+a%2F22+%29,highlight_red%28+2%2Aa+%29 replacing them with highlight_green%28+%281%2F22%2B2%29%2Aa+%29
It becomes highlight_green%28+%281%2F22%2B2%29%2Aa+%29-4.5=%281%29%2B%2817a%2F11%29.
Look at %28highlight_red%28+1%2F22+%29%2Bhighlight_red%28+2+%29%29%2Aa-4.5=%281%29%2B%2817a%2F11%29.
Added fractions or integers together
It becomes %28highlight_green%28+45%2F22+%29%29%2Aa-4.5=%281%29%2B%2817a%2F11%29.
Look at highlight_red%28+%28highlight_red%28+45%2F22+%29%29%2Aa+%29-4.5=%281%29%2B%2817a%2F11%29.
Remove unneeded parentheses around factor highlight_red%28+45+%29,highlight_red%28+1%2F22+%29
It becomes highlight_green%28+45+%29%2Fhighlight_green%28+22+%29%2Aa-4.5=%281%29%2B%2817a%2F11%29.
Look at 45%2F22%2Aa-4.5=highlight_red%28+%281%29+%29%2B%2817%2Aa%2F11%29.
Remove unneeded parentheses around terms highlight_red%28+1+%29
It becomes 45%2F22%2Aa-4.5=highlight_green%28+1+%29%2B%2817%2Aa%2F11%29.
Look at 45%2F22%2Aa-4.5=1%2Bhighlight_red%28+%2817%2Aa%2F11%29+%29.
Remove unneeded parentheses around terms highlight_red%28+17%2Aa%2F11+%29
It becomes 45%2F22%2Aa-4.5=1%2Bhighlight_green%28+17%2Aa%2F11+%29.
Look at 45%2F22%2Aa-4.5=highlight_red%28+1+%29%2B17%2Aa%2F11.
Moved 1 to the right of expression
It becomes 45%2F22%2Aa-4.5=17%2Aa%2F11%2Bhighlight_green%28+1+%29.
Look at 45%2F22%2Aa-4.5=highlight_red%28+17%2Aa%2F11%2B1+%29.
Moved these terms to the left highlight_green%28+-17%2Aa%2F11+%29,highlight_green%28+-1+%29
It becomes 45%2F22%2Aa-4.5-highlight_green%28+17%2Aa%2F11+%29-highlight_green%28+1+%29=0.
Look at 45%2F22%2Aa-highlight_red%28+4.5+%29-17%2Aa%2F11-highlight_red%28+1+%29=0.
Added fractions or integers together
It becomes 45%2F22%2Aa-highlight_green%28+55%2F10+%29-17%2Aa%2F11=0.
Look at 45%2F22%2Aa-highlight_red%28+55%2F10+%29-17%2Aa%2F11=0.
Moved -55%2F10 to the right of expression
It becomes 45%2F22%2Aa-17%2Aa%2F11-highlight_green%28+55%2F10+%29=0.
Look at 45%2F22%2Aa-17%2Aa%2F11-highlight_red%28+55+%29%2Fhighlight_red%28+10+%29=0.
Factors 55 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes 45%2F22%2Aa-17%2Aa%2F11-highlight_green%28+11+%29%2Fhighlight_green%28+2+%29=0.
Look at highlight_red%28+45%2F22%2Aa+%29-highlight_red%28+17%2Aa%2F11+%29-11%2F2=0.
Eliminated similar terms highlight_red%28+45%2F22%2Aa+%29,highlight_red%28+-17%2Aa%2F11+%29 replacing them with highlight_green%28+%2845%2A1%2F22-17%2A1%2F11%29%2Aa+%29
It becomes highlight_green%28+%2845%2A1%2F22-17%2A1%2F11%29%2Aa+%29-11%2F2=0.
Look at %28highlight_red%28+45+%29%2Ahighlight_red%28+1+%29%2F22-17%2A1%2F11%29%2Aa-11%2F2=0.
Multiplied numerator integers
It becomes %28highlight_green%28+45+%29%2F22-17%2A1%2F11%29%2Aa-11%2F2=0.
Look at %2845%2F22-highlight_red%28+17+%29%2Ahighlight_red%28+1+%29%2F11%29%2Aa-11%2F2=0.
Multiplied numerator integers
It becomes %2845%2F22-highlight_green%28+17+%29%2F11%29%2Aa-11%2F2=0.
Look at %28highlight_red%28+45%2F22+%29-highlight_red%28+17%2F11+%29%29%2Aa-11%2F2=0.
Added fractions or integers together
It becomes %28highlight_green%28+11%2F22+%29%29%2Aa-11%2F2=0.
Look at highlight_red%28+%28highlight_red%28+11%2F22+%29%29%2Aa+%29-11%2F2=0.
Remove unneeded parentheses around factor highlight_red%28+11+%29,highlight_red%28+1%2F22+%29
It becomes highlight_green%28+11+%29%2Fhighlight_green%28+22+%29%2Aa-11%2F2=0.
Look at highlight_red%28+11+%29%2Fhighlight_red%28+22+%29%2Aa-11%2F2=0.
Factors 11 and 22 have greatest common factor (GCF) of 11. Reducing fraction.
It becomes highlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2Aa-11%2F2=0.
Look at highlight_red%28+1+%29%2F2%2Aa-11%2F2=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes a%2F2-11%2F2=0.
Look at highlight_red%28+a%2F2-11%2F2+%29=0.
Solved linear equation highlight_red%28+a%2F2-11%2F2=0+%29 equivalent to 0.5*a-5.5 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=11.

Universal Simplifier and Solver


Done!


Hope this helps and feel free to contact me with further questions,
lyra