document.write( "Question 214176This question is from textbook
\n" ); document.write( ": find two consecutive odd integers such that their product is 15 more than 3 times their sum \n" ); document.write( "

Algebra.Com's Answer #161782 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find two consecutive odd integers such that their product is 15 more than 3 times their sum.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 1. Let n be an odd integer then n+2 be the next odd consecutive integer\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 2. n(n+2) is the product of the two odd integers.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 3. n+n+2 is the sum of the two odd integers.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 4. n(n+2)=15+3(n+n+2) product is 15 more than sum.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 5. Solve the equation in Step 4 using 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: n=7,n=-3.
Graphical form: Equation $\"n%2A%28n%2B2%29=15%2B3%2A%28n%2Bn%2B2%29\"$ was fully solved.
Text form: n*(n+2)=15+3*(n+n+2) simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+n%2A%28n%2B2%29=15%2B3%2A%28n%2Bn%2B2%29+%29\"$
For tutors: simplify_cartoon( n*(n+2)=15+3*(n+n+2) )
If you have a website, here's a link to this solution.

\n" ); document.write( "

DETAILED EXPLANATION

\n" ); document.write( "

Look at $\"n%2A%28n%2B2%29=highlight_red%28+15+%29%2B3%2A%28n%2Bn%2B2%29\"$ .
Moved $\"15\"$ to the right of expression
It becomes $\"n%2A%28n%2B2%29=3%2A%28n%2Bn%2B2%29%2Bhighlight_green%28+15+%29\"$ .
\n" ); document.write( "

Look at $\"n%2A%28n%2B2%29=3%2A%28highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B2%29%2B15\"$ .
Eliminated similar terms $\"highlight_red%28+n+%29\"$ , $\"highlight_red%28+n+%29\"$ replacing them with $\"highlight_green%28+%281%2B1%29%2An+%29\"$
It becomes $\"n%2A%28n%2B2%29=3%2A%28highlight_green%28+%281%2B1%29%2An+%29%2B2%29%2B15\"$ .
\n" ); document.write( "

Look at $\"n%2A%28n%2B2%29=3%2A%28%28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B2%29%2B15\"$ .
Added fractions or integers together
It becomes $\"n%2A%28n%2B2%29=3%2A%28%28highlight_green%28+2+%29%29%2An%2B2%29%2B15\"$ .
\n" ); document.write( "

Look at $\"n%2A%28n%2B2%29=3%2A%28highlight_red%28+%28highlight_red%28+2+%29%29%2An+%29%2B2%29%2B15\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"n%2A%28n%2B2%29=3%2A%28highlight_green%28+2+%29%2An%2B2%29%2B15\"$ .
\n" ); document.write( "

Look at $\"n%2A%28n%2B2%29=highlight_red%28+3%2A%282%2An%2B2%29%2B15+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-3%2A%282%2An%2B2%29+%29\"$ , $\"highlight_green%28+-15+%29\"$
It becomes $\"n%2A%28n%2B2%29-highlight_green%28+3%2A%282%2An%2B2%29+%29-highlight_green%28+15+%29=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+n%2A%28n%2B2%29+%29-3%2A%282%2An%2B2%29-15=0\"$ .
Expanded term $\"n\"$ by using associative property on $\"%28n%2B2%29\"$
It becomes $\"highlight_green%28+n%2An+%29%2Bhighlight_green%28+n%2A2+%29-3%2A%282%2An%2B2%29-15=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+n+%29%2Ahighlight_red%28+n+%29%2Bn%2A2-3%2A%282%2An%2B2%29-15=0\"$ .
Reduce similar several occurrences of $\"highlight_red%28+n+%29\"$ to $\"highlight_green%28+n%5E2+%29\"$
It becomes $\"highlight_green%28+n%5E2+%29%2Bn%2A2-3%2A%282%2An%2B2%29-15=0\"$ .
\n" ); document.write( "

Look at $\"n%5E2%2Bn%2A2-highlight_red%28+3%2A%282%2An%2B2%29+%29-15=0\"$ .
Expanded term $\"-3\"$ by using associative property on $\"%282%2An%2B2%29\"$
It becomes $\"n%5E2%2Bn%2A2-highlight_green%28+3%2A2%2An+%29-highlight_green%28+3%2A2+%29-15=0\"$ .
\n" ); document.write( "

Look at $\"n%5E2%2Bn%2A2-highlight_red%28+3+%29%2Ahighlight_red%28+2+%29%2An-3%2A2-15=0\"$ .
Multiplied numerator integers
It becomes $\"n%5E2%2Bn%2A2-highlight_green%28+6+%29%2An-3%2A2-15=0\"$ .
\n" ); document.write( "

Look at $\"n%5E2%2Bn%2A2-6%2An-highlight_red%28+3+%29%2Ahighlight_red%28+2+%29-15=0\"$ .
Multiplied numerator integers
It becomes $\"n%5E2%2Bn%2A2-6%2An-highlight_green%28+6+%29-15=0\"$ .
\n" ); document.write( "

Look at $\"n%5E2%2Bn%2A2-6%2An-highlight_red%28+6+%29-highlight_red%28+15+%29=0\"$ .
Added fractions or integers together
It becomes $\"n%5E2%2Bn%2A2-6%2An%2Bhighlight_green%28+-21+%29=0\"$ .
\n" ); document.write( "

Look at $\"n%5E2%2Bn%2A2-6%2An%2Bhighlight_red%28+-21+%29=0\"$ .
Removed extra sign in front of $\"-21\"$
It becomes $\"n%5E2%2Bn%2A2-6%2An-highlight_green%28+21+%29=0\"$ .
\n" ); document.write( "

Look at $\"n%5E2%2Bhighlight_red%28+n%2A2+%29-highlight_red%28+6%2An+%29-21=0\"$ .
Eliminated similar terms $\"highlight_red%28+n%2A2+%29\"$ , $\"highlight_red%28+-6%2An+%29\"$ replacing them with $\"highlight_green%28+%282-6%29%2An+%29\"$
It becomes $\"n%5E2%2Bhighlight_green%28+%282-6%29%2An+%29-21=0\"$ .
\n" ); document.write( "

Look at $\"n%5E2%2B%28highlight_red%28+2+%29-highlight_red%28+6+%29%29%2An-21=0\"$ .
Added fractions or integers together
It becomes $\"n%5E2%2B%28highlight_green%28+-4+%29%29%2An-21=0\"$ .
\n" ); document.write( "

Look at $\"n%5E2%2B%28highlight_red%28+-4+%29%29%2An-21=0\"$ .
Removed extra sign in front of $\"-4\"$
It becomes $\"n%5E2%2B%28-highlight_green%28+4+%29%29%2An-21=0\"$ .
\n" ); document.write( "

Look at $\"n%5E2%2Bhighlight_red%28+%28-highlight_red%28+4+%29%29%2An+%29-21=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+4+%29\"$
It becomes $\"n%5E2-highlight_green%28+4+%29%2An-21=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+n%5E2-4%2An-21+%29=0\"$ .
Equation $\"highlight_red%28+n%5E2-4%2An-21=0+%29\"$ is a quadratic equation: n^2-4*n-21 =0, and has solutions 7,-3
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=7,n=-3.

Universal Simplifier and Solver

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

\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 6. There are two solutions 7 and 9 is one solution set and the other -3 and -1 is another solution set.\r
\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 on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "And 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" );