SOLUTION: working with Real numbers. I need help with this problem: 3s + (-1/2)[6 + 24(-1/3 + 1/4s) please show your work and write it out how you did it in sentences so i can understand

Algebra ->  Real-numbers -> SOLUTION: working with Real numbers. I need help with this problem: 3s + (-1/2)[6 + 24(-1/3 + 1/4s) please show your work and write it out how you did it in sentences so i can understand      Log On


   

Question 6635: working with Real numbers.
I need help with this problem:
3s + (-1/2)[6 + 24(-1/3 + 1/4s)
please show your work and write it out how you did it in sentences so i can understand.
thanks alot
Answer by ichudov(507) 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: 3s%2B%28-1%2F2%29%2A%286%2B24%2A%28-1%2F3%2B1%2F4%2As%29%29 simplifies to 1
  • Text form: 3s+(-1/2)*(6+24*(-1/3+1/4*s)) simplifies to 1
  • Cartoon (animation) form: simplify_cartoon%28+3s%2B%28-1%2F2%29%2A%286%2B24%2A%28-1%2F3%2B1%2F4%2As%29%29+%29
    For tutors: simplify_cartoon( 3s+(-1/2)*(6+24*(-1/3+1/4*s)) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F2+%29
It becomes .
Look at 3%2As-highlight_red%28+1+%29%2F2%2A%286%2B24%2A%28-1%2F3%2B1%2F4%2As%29%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes 3%2As-%286%2B24%2A%28-1%2F3%2B1%2F4%2As%29%29%2F2.
Look at 3%2As-%286%2B24%2A%28-1%2F3%2Bhighlight_red%28+1+%29%2F4%2As%29%29%2F2.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes 3%2As-%286%2B24%2A%28-1%2F3%2Bs%2F4%29%29%2F2.
Look at 3%2As-%286%2B24%2A%28-highlight_red%28+1%2F3+%29%2Bs%2F4%29%29%2F2.
Moved -1%2F3 to the right of expression
It becomes 3%2As-%286%2B24%2A%28s%2F4-highlight_green%28+1%2F3+%29%29%29%2F2.
Look at 3%2As-%28highlight_red%28+6+%29%2B24%2A%28s%2F4-1%2F3%29%29%2F2.
Moved 6 to the right of expression
It becomes 3%2As-%2824%2A%28s%2F4-1%2F3%29%2Bhighlight_green%28+6+%29%29%2F2.
Look at 3%2As-%28highlight_red%28+24%2A%28s%2F4-1%2F3%29+%29%2B6%29%2F2.
Expanded term 24 by using associative property on %28s%2F4-1%2F3%29
It becomes 3%2As-%28highlight_green%28+24%2As%2F4+%29-highlight_green%28+24%2A1%2F3+%29%2B6%29%2F2.
Look at 3%2As-highlight_red%28+%2824%2As%2F4-24%2A1%2F3%2B6%29%2F2+%29.
Expanded term -1%2F2 by using associative property on %2824%2As%2F4-24%2A1%2F3%2B6%29
It becomes .
Look at .
Factors 24 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .
Look at .
Factors 12 and 4 have greatest common factor (GCF) of 4. Reducing fraction.
It becomes .
Look at .
Multiplied numerator integers
It becomes 3%2As-highlight_green%28+3+%29%2F1%2As%2F1%2B1%2F2%2A24%2A1%2F3-1%2F2%2A6.
Look at 3%2As-3%2Fhighlight_red%28+1+%29%2As%2Fhighlight_red%28+1+%29%2B1%2F2%2A24%2A1%2F3-1%2F2%2A6.
Multiplied denominator integers
It becomes 3%2As-3%2Fhighlight_green%28+1+%29%2As%2B1%2F2%2A24%2A1%2F3-1%2F2%2A6.
Look at 3%2As-3%2F1%2As%2B1%2Fhighlight_red%28+2+%29%2Ahighlight_red%28+24+%29%2A1%2F3-1%2F2%2A6.
Factors 24 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 3%2As-3%2F1%2As%2B1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+12+%29%2A1%2F3-1%2F2%2A6.
Look at 3%2As-3%2F1%2As%2B1%2F1%2Ahighlight_red%28+12+%29%2A1%2Fhighlight_red%28+3+%29-1%2F2%2A6.
Factors 12 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes 3%2As-3%2F1%2As%2B1%2F1%2Ahighlight_green%28+4+%29%2A1%2Fhighlight_green%28+1+%29-1%2F2%2A6.
Look at .
Multiplied numerator integers
It becomes 3%2As-3%2F1%2As%2Bhighlight_green%28+4+%29%2F1%2F1-1%2F2%2A6.
Look at 3%2As-3%2F1%2As%2B4%2Fhighlight_red%28+1+%29%2Fhighlight_red%28+1+%29-1%2F2%2A6.
Multiplied denominator integers
It becomes 3%2As-3%2F1%2As%2B4%2Fhighlight_green%28+1+%29-1%2F2%2A6.
Look at 3%2As-3%2F1%2As%2B4%2F1-1%2Fhighlight_red%28+2+%29%2Ahighlight_red%28+6+%29.
Factors 6 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 3%2As-3%2F1%2As%2B4%2F1-1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+3+%29.
Look at 3%2As-3%2F1%2As%2B4%2F1-highlight_red%28+1+%29%2F1%2Ahighlight_red%28+3+%29.
Multiplied numerator integers
It becomes 3%2As-3%2F1%2As%2B4%2F1-highlight_green%28+3+%29%2F1.
Look at 3%2As-3%2F1%2As%2Bhighlight_red%28+4%2F1+%29-highlight_red%28+3%2F1+%29.
Added fractions or integers together
It becomes 3%2As-3%2F1%2As%2Bhighlight_green%28+1+%29.
Look at 3%2As-3%2Fhighlight_red%28+1+%29%2As%2B1.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 3%2As-3%2As%2B1.
Look at highlight_red%28+3%2As+%29-highlight_red%28+3%2As+%29%2B1.
Eliminated similar terms highlight_red%28+3%2As+%29,highlight_red%28+-3%2As+%29 replacing them with highlight_green%28+%283-3%29%2As+%29
It becomes highlight_green%28+%283-3%29%2As+%29%2B1.
Look at highlight_red%28+%283-3%29%2As+%29%2B1.
Since highlight_red%28+%283-3%29%2As+%29 has zero as a factor, it should be replaced with a zero
Look at 0%2B1.
Added fractions or integers together
It becomes 0%2B1.
Look at highlight_red%28+0+%29%2B1.
Remove extraneous zero highlight_red%28+0+%29
It becomes 1.
Result: 1

Universal Simplifier and Solver


Done!