document.write( "Question 215304: One number is 8 less than another number. Find the numbers if three times the smaller number is six less than two times the larger number \n" ); document.write( "

Algebra.Com's Answer #162699 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
One number is 8 less than another number. Find the numbers if three times the smaller number is six less than two times the larger number\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let x be the smaller number and x+8 be the larger number\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let 3x be three times the smaller number.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 2(x+8) be two times the larger number.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Since three times the smaller number is six less than two times the larger number, then $\"3x=2%28x%2B8%29-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Step 5. Solving the equation in Step 4 yields the following steps.\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=10.
Graphical form: Equation $\"3x=2%2A%28x%2B8%29-6\"$ was fully solved.
Text form: 3x=2*(x+8)-6 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+3x=2%2A%28x%2B8%29-6+%29\"$
For tutors: simplify_cartoon( 3x=2*(x+8)-6 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"3%2Ax=highlight_red%28+2%2A%28x%2B8%29-6+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-2%2A%28x%2B8%29+%29\"$ , $\"highlight_green%28+6+%29\"$
It becomes $\"3%2Ax-highlight_green%28+2%2A%28x%2B8%29+%29%2Bhighlight_green%28+6+%29=0\"$ .
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Look at $\"3%2Ax-highlight_red%28+2%2A%28x%2B8%29+%29%2B6=0\"$ .
Expanded term $\"-2\"$ by using associative property on $\"%28x%2B8%29\"$
It becomes $\"3%2Ax-highlight_green%28+2%2Ax+%29-highlight_green%28+2%2A8+%29%2B6=0\"$ .
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Look at $\"3%2Ax-2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+8+%29%2B6=0\"$ .
Multiplied numerator integers
It becomes $\"3%2Ax-2%2Ax-highlight_green%28+16+%29%2B6=0\"$ .
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Look at $\"3%2Ax-2%2Ax-highlight_red%28+16+%29%2Bhighlight_red%28+6+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2Ax-2%2Ax%2Bhighlight_green%28+-10+%29=0\"$ .
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Look at $\"3%2Ax-2%2Ax%2Bhighlight_red%28+-10+%29=0\"$ .
Removed extra sign in front of $\"-10\"$
It becomes $\"3%2Ax-2%2Ax-highlight_green%28+10+%29=0\"$ .
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Look at $\"highlight_red%28+3%2Ax+%29-highlight_red%28+2%2Ax+%29-10=0\"$ .
Eliminated similar terms $\"highlight_red%28+3%2Ax+%29\"$ , $\"highlight_red%28+-2%2Ax+%29\"$ replacing them with $\"highlight_green%28+%283-2%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%283-2%29%2Ax+%29-10=0\"$ .
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Look at $\"highlight_red%28+%283-2%29+%29%2Ax-10=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+%283-2%29+%29\"$
It becomes $\"x-10=0\"$ .
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Look at $\"highlight_red%28+x-10+%29=0\"$ .
Solved linear equation $\"highlight_red%28+x-10=0+%29\"$ equivalent to x-10 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=10.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=10 , then x+8=18\r
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\n" ); document.write( "\n" ); document.write( "Step 6. ANSWER: The numbers are 10 and 18.\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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