document.write( "Question 216456: 5(2k + 6) + 2(1 - 3k) = 60 \n" ); document.write( "
Algebra.Com's Answer #163425 by drj(1380)\"\" \"About 
You can put this solution on YOUR website!
\"5%282k+%2B+6%29+%2B+2%281+-+3k%29+=+60+\"\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • This is an equation! Solutions: k=7.
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  • Graphical form: Equation \"5%2A%282k%2B6%29%2B2%2A%281-3k%29=60\" was fully solved.
  • Text form: 5*(2k+6)+2*(1-3k)=60 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+5%2A%282k%2B6%29%2B2%2A%281-3k%29=60+%29\"
    For tutors: simplify_cartoon( 5*(2k+6)+2*(1-3k)=60 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"5%2A%282%2Ak%2B6%29%2B2%2A%28highlight_red%28+1+%29-3%2Ak%29=60\".
Moved \"1\" to the right of expression
It becomes \"5%2A%282%2Ak%2B6%29%2B2%2A%28-3%2Ak%2Bhighlight_green%28+1+%29%29=60\".
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Look at \"5%2A%282%2Ak%2B6%29%2B2%2A%28-3%2Ak%2B1%29=highlight_red%28+60+%29\".
Moved these terms to the left \"highlight_green%28+-60+%29\"
It becomes \"5%2A%282%2Ak%2B6%29%2B2%2A%28-3%2Ak%2B1%29-highlight_green%28+60+%29=0\".
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Look at \"highlight_red%28+5%2A%282%2Ak%2B6%29+%29%2B2%2A%28-3%2Ak%2B1%29-60=0\".
Expanded term \"5\" by using associative property on \"%282%2Ak%2B6%29\"
It becomes \"highlight_green%28+5%2A2%2Ak+%29%2Bhighlight_green%28+5%2A6+%29%2B2%2A%28-3%2Ak%2B1%29-60=0\".
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Look at \"highlight_red%28+5+%29%2Ahighlight_red%28+2+%29%2Ak%2B5%2A6%2B2%2A%28-3%2Ak%2B1%29-60=0\".
Multiplied numerator integers
It becomes \"highlight_green%28+10+%29%2Ak%2B5%2A6%2B2%2A%28-3%2Ak%2B1%29-60=0\".
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Look at \"10%2Ak%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+6+%29%2B2%2A%28-3%2Ak%2B1%29-60=0\".
Multiplied numerator integers
It becomes \"10%2Ak%2Bhighlight_green%28+30+%29%2B2%2A%28-3%2Ak%2B1%29-60=0\".
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Look at \"10%2Ak%2Bhighlight_red%28+30+%29%2B2%2A%28-3%2Ak%2B1%29-highlight_red%28+60+%29=0\".
Added fractions or integers together
It becomes \"10%2Ak%2Bhighlight_green%28+-30+%29%2B2%2A%28-3%2Ak%2B1%29=0\".
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Look at \"10%2Ak%2Bhighlight_red%28+-30+%29%2B2%2A%28-3%2Ak%2B1%29=0\".
Moved \"-30\" to the right of expression
It becomes \"10%2Ak%2B2%2A%28-3%2Ak%2B1%29%2Bhighlight_green%28+-30+%29=0\".
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Look at \"10%2Ak%2B2%2A%28-3%2Ak%2B1%29%2Bhighlight_red%28+-30+%29=0\".
Removed extra sign in front of \"-30\"
It becomes \"10%2Ak%2B2%2A%28-3%2Ak%2B1%29-highlight_green%28+30+%29=0\".
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Look at \"10%2Ak%2Bhighlight_red%28+2%2A%28-3%2Ak%2B1%29+%29-30=0\".
Expanded term \"2\" by using associative property on \"%28-3%2Ak%2B1%29\"
It becomes \"10%2Ak-highlight_green%28+2%2A3%2Ak+%29%2Bhighlight_green%28+2%2A1+%29-30=0\".
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Look at \"10%2Ak-highlight_red%28+2+%29%2Ahighlight_red%28+3+%29%2Ak%2B2%2A1-30=0\".
Multiplied numerator integers
It becomes \"10%2Ak-highlight_green%28+6+%29%2Ak%2B2%2A1-30=0\".
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Look at \"10%2Ak-6%2Ak%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29-30=0\".
Multiplied numerator integers
It becomes \"10%2Ak-6%2Ak%2Bhighlight_green%28+2+%29-30=0\".
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Look at \"10%2Ak-6%2Ak%2Bhighlight_red%28+2+%29-highlight_red%28+30+%29=0\".
Added fractions or integers together
It becomes \"10%2Ak-6%2Ak%2Bhighlight_green%28+-28+%29=0\".
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Look at \"10%2Ak-6%2Ak%2Bhighlight_red%28+-28+%29=0\".
Removed extra sign in front of \"-28\"
It becomes \"10%2Ak-6%2Ak-highlight_green%28+28+%29=0\".
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Look at \"highlight_red%28+10%2Ak+%29-highlight_red%28+6%2Ak+%29-28=0\".
Eliminated similar terms \"highlight_red%28+10%2Ak+%29\",\"highlight_red%28+-6%2Ak+%29\" replacing them with \"highlight_green%28+%2810-6%29%2Ak+%29\"
It becomes \"highlight_green%28+%2810-6%29%2Ak+%29-28=0\".
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Look at \"%28highlight_red%28+10+%29-highlight_red%28+6+%29%29%2Ak-28=0\".
Added fractions or integers together
It becomes \"%28highlight_green%28+4+%29%29%2Ak-28=0\".
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Look at \"highlight_red%28+%28highlight_red%28+4+%29%29%2Ak+%29-28=0\".
Remove unneeded parentheses around factor \"highlight_red%28+4+%29\"
It becomes \"highlight_green%28+4+%29%2Ak-28=0\".
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Look at \"highlight_red%28+4%2Ak-28+%29=0\".
Solved linear equation \"highlight_red%28+4%2Ak-28=0+%29\" equivalent to 4*k-28 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
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Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "I hope the above steps and explanation were helpful. \r
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\n" ); document.write( "\n" ); document.write( "For Step-By-Step videos on Introduction to Algebra, \r
\n" ); document.write( "\n" ); document.write( "please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and \r
\n" ); document.write( "\n" ); document.write( "for Trigonmetry please visit \r
\n" ); document.write( "\n" ); document.write( "http://www.FreedomUniversity.TV/courses/Trigonometry. \r
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\n" ); document.write( "\n" ); document.write( "Also, good luck in your studies and contact me at \r
\n" ); document.write( "\n" ); document.write( "john@e-liteworks.com for your future math needs.\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J \n" ); document.write( "
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