document.write( "Question 223660: The sum of two numbers is twelve. The total of three times the smaller number and six amounts to seven less than the product of four and the larger number. Find the two numbers. \n" ); document.write( "

Algebra.Com's Answer #167183 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
The sum of two numbers is twelve. The total of three times the smaller number and six amounts to seven less than the product of four and the larger number. Find the two numbers.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 1. Let x be one number\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 2. Let 12-x be the other number\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 3. 3x+6=4*(12-x)-7 since the total of three times the smaller number and six amounts to seven less than the product of four and the larger number.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 4. Solving yields the following steps\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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

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

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

This is an equation! Solutions: x=5.
Graphical form: Equation $\"3x%2B6=4%2A%2812-x%29-7\"$ was fully solved.
Text form: 3x+6=4*(12-x)-7 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+3x%2B6=4%2A%2812-x%29-7+%29\"$
For tutors: simplify_cartoon( 3x+6=4*(12-x)-7 )
If you have a website, here's a link to this solution.

\n" ); document.write( "

DETAILED EXPLANATION

\n" ); document.write( "

Look at $\"3%2Ax%2B6=4%2A%28highlight_red%28+12+%29-x%29-7\"$ .
Moved $\"12\"$ to the right of expression
It becomes $\"3%2Ax%2B6=4%2A%28-x%2Bhighlight_green%28+12+%29%29-7\"$ .
\n" ); document.write( "

Look at $\"3%2Ax%2B6=highlight_red%28+4%2A%28-x%2B12%29-7+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-4%2A%28-x%2B12%29+%29\"$ , $\"highlight_green%28+7+%29\"$
It becomes $\"3%2Ax%2B6-highlight_green%28+4%2A%28-x%2B12%29+%29%2Bhighlight_green%28+7+%29=0\"$ .
\n" ); document.write( "

Look at $\"3%2Ax%2Bhighlight_red%28+6+%29-4%2A%28-x%2B12%29%2Bhighlight_red%28+7+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2Ax%2Bhighlight_green%28+13+%29-4%2A%28-x%2B12%29=0\"$ .
\n" ); document.write( "

Look at $\"3%2Ax%2Bhighlight_red%28+13+%29-4%2A%28-x%2B12%29=0\"$ .
Moved $\"13\"$ to the right of expression
It becomes $\"3%2Ax-4%2A%28-x%2B12%29%2Bhighlight_green%28+13+%29=0\"$ .
\n" ); document.write( "

Look at $\"3%2Ax-highlight_red%28+4%2A%28-x%2B12%29+%29%2B13=0\"$ .
Expanded term $\"-4\"$ by using associative property on $\"%28-x%2B12%29\"$
It becomes $\"3%2Ax%2Bhighlight_green%28+4%2Ax+%29-highlight_green%28+4%2A12+%29%2B13=0\"$ .
\n" ); document.write( "

Look at $\"3%2Ax%2B4%2Ax-highlight_red%28+4+%29%2Ahighlight_red%28+12+%29%2B13=0\"$ .
Multiplied numerator integers
It becomes $\"3%2Ax%2B4%2Ax-highlight_green%28+48+%29%2B13=0\"$ .
\n" ); document.write( "

Look at $\"3%2Ax%2B4%2Ax-highlight_red%28+48+%29%2Bhighlight_red%28+13+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2Ax%2B4%2Ax%2Bhighlight_green%28+-35+%29=0\"$ .
\n" ); document.write( "

Look at $\"3%2Ax%2B4%2Ax%2Bhighlight_red%28+-35+%29=0\"$ .
Removed extra sign in front of $\"-35\"$
It becomes $\"3%2Ax%2B4%2Ax-highlight_green%28+35+%29=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+3%2Ax+%29%2Bhighlight_red%28+4%2Ax+%29-35=0\"$ .
Eliminated similar terms $\"highlight_red%28+3%2Ax+%29\"$ , $\"highlight_red%28+4%2Ax+%29\"$ replacing them with $\"highlight_green%28+%283%2B4%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%283%2B4%29%2Ax+%29-35=0\"$ .
\n" ); document.write( "

Look at $\"%28highlight_red%28+3+%29%2Bhighlight_red%28+4+%29%29%2Ax-35=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+7+%29%29%2Ax-35=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+%28highlight_red%28+7+%29%29%2Ax+%29-35=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+7+%29\"$
It becomes $\"highlight_green%28+7+%29%2Ax-35=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+7%2Ax-35+%29=0\"$ .
Solved linear equation $\"highlight_red%28+7%2Ax-35=0+%29\"$ equivalent to 7*x-35 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=5.

Universal Simplifier and Solver

\n" ); document.write( "
Done!

\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "With x=5, then 12-5=7\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Check... $\"3x%2B6=4%2A%2812-x%29-7\"$ or $\"3%2A5%2B6=4%2A7-7\"$ which is a true statement.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 5. ANSWER: The numbers are 5 and 7\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Good luck in your studies!\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );