document.write( "Question 586648: Solve and check. Label any contradictions or identities.
\n" ); document.write( "5(t+1)+8=3(t-2)+6 \n" ); document.write( "
Algebra.Com's Answer #373842 by eschwartz(9)\"\" \"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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  • This is an equation! Solutions: t=-6.5.
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  • Graphical form: Equation \"5%2A%28t%2B1%29%2B8=3%2A%28t-2%29%2B6\" was fully solved.
  • Text form: 5*(t+1)+8=3*(t-2)+6 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+5%2A%28t%2B1%29%2B8=3%2A%28t-2%29%2B6+%29\"
    For tutors: simplify_cartoon( 5*(t+1)+8=3*(t-2)+6 )
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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%28t%2B1%29%2B8=highlight_red%28+3%2A%28t-2%29%2B6+%29\".
Moved these terms to the left \"highlight_green%28+-3%2A%28t-2%29+%29\",\"highlight_green%28+-6+%29\"
It becomes \"5%2A%28t%2B1%29%2B8-highlight_green%28+3%2A%28t-2%29+%29-highlight_green%28+6+%29=0\".
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Look at \"5%2A%28t%2B1%29%2Bhighlight_red%28+8+%29-3%2A%28t-2%29-highlight_red%28+6+%29=0\".
Added fractions or integers together
It becomes \"5%2A%28t%2B1%29%2Bhighlight_green%28+2+%29-3%2A%28t-2%29=0\".
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Look at \"5%2A%28t%2B1%29%2Bhighlight_red%28+2+%29-3%2A%28t-2%29=0\".
Moved \"2\" to the right of expression
It becomes \"5%2A%28t%2B1%29-3%2A%28t-2%29%2Bhighlight_green%28+2+%29=0\".
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Look at \"highlight_red%28+5%2A%28t%2B1%29+%29-3%2A%28t-2%29%2B2=0\".
Expanded term \"5\" by using associative property on \"%28t%2B1%29\"
It becomes \"highlight_green%28+5%2At+%29%2Bhighlight_green%28+5%2A1+%29-3%2A%28t-2%29%2B2=0\".
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Look at \"5%2At%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+1+%29-3%2A%28t-2%29%2B2=0\".
Multiplied numerator integers
It becomes \"5%2At%2Bhighlight_green%28+5+%29-3%2A%28t-2%29%2B2=0\".
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Look at \"5%2At%2Bhighlight_red%28+5+%29-3%2A%28t-2%29%2Bhighlight_red%28+2+%29=0\".
Added fractions or integers together
It becomes \"5%2At%2Bhighlight_green%28+7+%29-3%2A%28t-2%29=0\".
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Look at \"5%2At%2Bhighlight_red%28+7+%29-3%2A%28t-2%29=0\".
Moved \"7\" to the right of expression
It becomes \"5%2At-3%2A%28t-2%29%2Bhighlight_green%28+7+%29=0\".
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Look at \"5%2At-highlight_red%28+3%2A%28t-2%29+%29%2B7=0\".
Expanded term \"-3\" by using associative property on \"%28t-2%29\"
It becomes \"5%2At-highlight_green%28+3%2At+%29%2Bhighlight_green%28+3%2A2+%29%2B7=0\".
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Look at \"5%2At-3%2At%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+2+%29%2B7=0\".
Multiplied numerator integers
It becomes \"5%2At-3%2At%2Bhighlight_green%28+6+%29%2B7=0\".
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Look at \"5%2At-3%2At%2Bhighlight_red%28+6+%29%2Bhighlight_red%28+7+%29=0\".
Added fractions or integers together
It becomes \"5%2At-3%2At%2Bhighlight_green%28+13+%29=0\".
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Look at \"highlight_red%28+5%2At+%29-highlight_red%28+3%2At+%29%2B13=0\".
Eliminated similar terms \"highlight_red%28+5%2At+%29\",\"highlight_red%28+-3%2At+%29\" replacing them with \"highlight_green%28+%285-3%29%2At+%29\"
It becomes \"highlight_green%28+%285-3%29%2At+%29%2B13=0\".
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Look at \"%28highlight_red%28+5+%29-highlight_red%28+3+%29%29%2At%2B13=0\".
Added fractions or integers together
It becomes \"%28highlight_green%28+2+%29%29%2At%2B13=0\".
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Look at \"highlight_red%28+%28highlight_red%28+2+%29%29%2At+%29%2B13=0\".
Remove unneeded parentheses around factor \"highlight_red%28+2+%29\"
It becomes \"highlight_green%28+2+%29%2At%2B13=0\".
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Look at \"highlight_red%28+2%2At%2B13+%29=0\".
Solved linear equation \"highlight_red%28+2%2At%2B13=0+%29\" equivalent to 2*t+13 =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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