document.write( "Question 213745: -4(a+1)-3a=7(2a-3)+3 \n" ); document.write( "

Algebra.Com's Answer #161480 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"-4%28a%2B1%29-3a=7%282a-3%29%2B3\"$ \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: a=0.666666666666667.
Graphical form: Equation $\"-4%2A%28a%2B1%29-3a=7%2A%282a-3%29%2B3\"$ was fully solved.
Text form: -4*(a+1)-3a=7*(2a-3)+3 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+-4%2A%28a%2B1%29-3a=7%2A%282a-3%29%2B3+%29\"$
For tutors: simplify_cartoon( -4*(a+1)-3a=7*(2a-3)+3 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"-4%2A%28a%2B1%29-3%2Aa=highlight_red%28+7%2A%282%2Aa-3%29%2B3+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-7%2A%282%2Aa-3%29+%29\"$ , $\"highlight_green%28+-3+%29\"$
It becomes $\"-4%2A%28a%2B1%29-3%2Aa-highlight_green%28+7%2A%282%2Aa-3%29+%29-highlight_green%28+3+%29=0\"$ .
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Look at $\"-highlight_red%28+4%2A%28a%2B1%29+%29-3%2Aa-7%2A%282%2Aa-3%29-3=0\"$ .
Expanded term $\"-4\"$ by using associative property on $\"%28a%2B1%29\"$
It becomes $\"-highlight_green%28+4%2Aa+%29-highlight_green%28+4%2A1+%29-3%2Aa-7%2A%282%2Aa-3%29-3=0\"$ .
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Look at $\"-4%2Aa-highlight_red%28+4+%29%2Ahighlight_red%28+1+%29-3%2Aa-7%2A%282%2Aa-3%29-3=0\"$ .
Multiplied numerator integers
It becomes $\"-4%2Aa-highlight_green%28+4+%29-3%2Aa-7%2A%282%2Aa-3%29-3=0\"$ .
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Look at $\"-4%2Aa-highlight_red%28+4+%29-3%2Aa-7%2A%282%2Aa-3%29-highlight_red%28+3+%29=0\"$ .
Added fractions or integers together
It becomes $\"-4%2Aa%2Bhighlight_green%28+-7+%29-3%2Aa-7%2A%282%2Aa-3%29=0\"$ .
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Look at $\"-4%2Aa%2Bhighlight_red%28+-7+%29-3%2Aa-7%2A%282%2Aa-3%29=0\"$ .
Moved $\"-7\"$ to the right of expression
It becomes $\"-4%2Aa-3%2Aa-7%2A%282%2Aa-3%29%2Bhighlight_green%28+-7+%29=0\"$ .
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Look at $\"-4%2Aa-3%2Aa-7%2A%282%2Aa-3%29%2Bhighlight_red%28+-7+%29=0\"$ .
Removed extra sign in front of $\"-7\"$
It becomes $\"-4%2Aa-3%2Aa-7%2A%282%2Aa-3%29-highlight_green%28+7+%29=0\"$ .
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Look at $\"-highlight_red%28+4%2Aa+%29-highlight_red%28+3%2Aa+%29-7%2A%282%2Aa-3%29-7=0\"$ .
Eliminated similar terms $\"highlight_red%28+-4%2Aa+%29\"$ , $\"highlight_red%28+-3%2Aa+%29\"$ replacing them with $\"highlight_green%28+%28-4-3%29%2Aa+%29\"$
It becomes $\"highlight_green%28+%28-4-3%29%2Aa+%29-7%2A%282%2Aa-3%29-7=0\"$ .
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Look at $\"%28-highlight_red%28+4+%29-highlight_red%28+3+%29%29%2Aa-7%2A%282%2Aa-3%29-7=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-7+%29%29%2Aa-7%2A%282%2Aa-3%29-7=0\"$ .
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Look at $\"%28highlight_red%28+-7+%29%29%2Aa-7%2A%282%2Aa-3%29-7=0\"$ .
Removed extra sign in front of $\"-7\"$
It becomes $\"%28-highlight_green%28+7+%29%29%2Aa-7%2A%282%2Aa-3%29-7=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+7+%29%29%2Aa+%29-7%2A%282%2Aa-3%29-7=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+7+%29\"$
It becomes $\"-highlight_green%28+7+%29%2Aa-7%2A%282%2Aa-3%29-7=0\"$ .
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Look at $\"-7%2Aa-highlight_red%28+7%2A%282%2Aa-3%29+%29-7=0\"$ .
Expanded term $\"-7\"$ by using associative property on $\"%282%2Aa-3%29\"$
It becomes $\"-7%2Aa-highlight_green%28+7%2A2%2Aa+%29%2Bhighlight_green%28+7%2A3+%29-7=0\"$ .
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Look at $\"-7%2Aa-highlight_red%28+7+%29%2Ahighlight_red%28+2+%29%2Aa%2B7%2A3-7=0\"$ .
Multiplied numerator integers
It becomes $\"-7%2Aa-highlight_green%28+14+%29%2Aa%2B7%2A3-7=0\"$ .
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Look at $\"-7%2Aa-14%2Aa%2Bhighlight_red%28+7+%29%2Ahighlight_red%28+3+%29-7=0\"$ .
Multiplied numerator integers
It becomes $\"-7%2Aa-14%2Aa%2Bhighlight_green%28+21+%29-7=0\"$ .
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Look at $\"-7%2Aa-14%2Aa%2Bhighlight_red%28+21+%29-highlight_red%28+7+%29=0\"$ .
Added fractions or integers together
It becomes $\"-7%2Aa-14%2Aa%2Bhighlight_green%28+14+%29=0\"$ .
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Look at $\"-highlight_red%28+7%2Aa+%29-highlight_red%28+14%2Aa+%29%2B14=0\"$ .
Eliminated similar terms $\"highlight_red%28+-7%2Aa+%29\"$ , $\"highlight_red%28+-14%2Aa+%29\"$ replacing them with $\"highlight_green%28+%28-7-14%29%2Aa+%29\"$
It becomes $\"highlight_green%28+%28-7-14%29%2Aa+%29%2B14=0\"$ .
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Look at $\"%28-highlight_red%28+7+%29-highlight_red%28+14+%29%29%2Aa%2B14=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-21+%29%29%2Aa%2B14=0\"$ .
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Look at $\"%28highlight_red%28+-21+%29%29%2Aa%2B14=0\"$ .
Removed extra sign in front of $\"-21\"$
It becomes $\"%28-highlight_green%28+21+%29%29%2Aa%2B14=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+21+%29%29%2Aa+%29%2B14=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+21+%29\"$
It becomes $\"-highlight_green%28+21+%29%2Aa%2B14=0\"$ .
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Look at $\"highlight_red%28+-21%2Aa%2B14+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-21%2Aa%2B14=0+%29\"$ equivalent to -21*a+14 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: a=0.666666666666667.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "ANSWER is $\"2%2F3\"$ or 0.666667\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
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\n" ); document.write( "\n" ); document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r
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\n" ); document.write( "\n" ); document.write( "Good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J \n" ); document.write( "

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