document.write( "Question 6635: working with Real numbers.
\n" ); document.write( "I need help with this problem:
\n" ); document.write( "3s + (-1/2)[6 + 24(-1/3 + 1/4s)
\n" ); document.write( " please show your work and write it out how you did it in sentences so i can understand.
\n" ); document.write( "thanks alot \n" ); document.write( "

Algebra.Com's Answer #3608 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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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.

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DETAILED EXPLANATION

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Look at

.
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$ , $\"highlight_red%28+1%2F2+%29\"$
It becomes

.
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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 $\"3%2As-%286%2B24%2A%28-1%2F3%2B1%2F4%2As%29%29%2F2\"$ .
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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 $\"3%2As-%286%2B24%2A%28-1%2F3%2Bs%2F4%29%29%2F2\"$ .
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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 $\"3%2As-%286%2B24%2A%28s%2F4-highlight_green%28+1%2F3+%29%29%29%2F2\"$ .
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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 $\"3%2As-%2824%2A%28s%2F4-1%2F3%29%2Bhighlight_green%28+6+%29%29%2F2\"$ .
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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 $\"3%2As-%28highlight_green%28+24%2As%2F4+%29-highlight_green%28+24%2A1%2F3+%29%2B6%29%2F2\"$ .
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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

.
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Look at

.
Factors 24 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes

.
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Look at

.
Factors 12 and 4 have greatest common factor (GCF) of 4. Reducing fraction.
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"3%2As-highlight_green%28+3+%29%2F1%2As%2F1%2B1%2F2%2A24%2A1%2F3-1%2F2%2A6\"$ .
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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 $\"3%2As-3%2Fhighlight_green%28+1+%29%2As%2B1%2F2%2A24%2A1%2F3-1%2F2%2A6\"$ .
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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 $\"3%2As-3%2F1%2As%2B1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+12+%29%2A1%2F3-1%2F2%2A6\"$ .
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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 $\"3%2As-3%2F1%2As%2B1%2F1%2Ahighlight_green%28+4+%29%2A1%2Fhighlight_green%28+1+%29-1%2F2%2A6\"$ .
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Look at

.
Multiplied numerator integers
It becomes $\"3%2As-3%2F1%2As%2Bhighlight_green%28+4+%29%2F1%2F1-1%2F2%2A6\"$ .
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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 $\"3%2As-3%2F1%2As%2B4%2Fhighlight_green%28+1+%29-1%2F2%2A6\"$ .
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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 $\"3%2As-3%2F1%2As%2B4%2F1-1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+3+%29\"$ .
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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 $\"3%2As-3%2F1%2As%2B4%2F1-highlight_green%28+3+%29%2F1\"$ .
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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 $\"3%2As-3%2F1%2As%2Bhighlight_green%28+1+%29\"$ .
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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 $\"3%2As-3%2As%2B1\"$ .
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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 $\"highlight_green%28+%283-3%29%2As+%29%2B1\"$ .
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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
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Look at $\"0%2B1\"$ .
Added fractions or integers together
It becomes $\"0%2B1\"$ .
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Look at $\"highlight_red%28+0+%29%2B1\"$ .
Remove extraneous zero $\"highlight_red%28+0+%29\"$
It becomes $\"1\"$ .
Result: $\"1\"$
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Universal Simplifier and Solver

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Done!

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