document.write( "Question 223711: the sum of of four times a number and three is the same as the difference of twice the number and eleven.find the number \n" ); document.write( "

Algebra.Com's Answer #167201 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
The the sum of of four times a number and three is the same as the difference of twice the number and eleven. Find the number.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let x be a number\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let 4x+3 be the sum of four times a number and three.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 2x-11 be the difference of twice the number and eleven.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Set Steps 2 and 3 to be equal: $\"4x%2B3=2x-11\"$ since the the sum of of four times a number and three is the same as the difference of twice the number and eleven.\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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This is an equation! Solutions: x=-7.
Graphical form: Equation $\"4x%2B3=2x-11\"$ was fully solved.
Text form: 4x+3=2x-11 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+4x%2B3=2x-11+%29\"$
For tutors: simplify_cartoon( 4x+3=2x-11 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"4%2Ax%2B3=highlight_red%28+2%2Ax-11+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-2%2Ax+%29\"$ , $\"highlight_green%28+11+%29\"$
It becomes $\"4%2Ax%2B3-highlight_green%28+2%2Ax+%29%2Bhighlight_green%28+11+%29=0\"$ .
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Look at $\"4%2Ax%2Bhighlight_red%28+3+%29-2%2Ax%2Bhighlight_red%28+11+%29=0\"$ .
Added fractions or integers together
It becomes $\"4%2Ax%2Bhighlight_green%28+14+%29-2%2Ax=0\"$ .
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Look at $\"4%2Ax%2Bhighlight_red%28+14+%29-2%2Ax=0\"$ .
Moved $\"14\"$ to the right of expression
It becomes $\"4%2Ax-2%2Ax%2Bhighlight_green%28+14+%29=0\"$ .
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Look at $\"highlight_red%28+4%2Ax+%29-highlight_red%28+2%2Ax+%29%2B14=0\"$ .
Eliminated similar terms $\"highlight_red%28+4%2Ax+%29\"$ , $\"highlight_red%28+-2%2Ax+%29\"$ replacing them with $\"highlight_green%28+%284-2%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%284-2%29%2Ax+%29%2B14=0\"$ .
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Look at $\"%28highlight_red%28+4+%29-highlight_red%28+2+%29%29%2Ax%2B14=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+2+%29%29%2Ax%2B14=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+2+%29%29%2Ax+%29%2B14=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"highlight_green%28+2+%29%2Ax%2B14=0\"$ .
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Look at $\"highlight_red%28+2%2Ax%2B14+%29=0\"$ .
Solved linear equation $\"highlight_red%28+2%2Ax%2B14=0+%29\"$ equivalent to 2*x+14 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=-7.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "Step 5. ANSWER: The number is -7.\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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