document.write( "Question 226000: For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers? \n" ); document.write( "

Algebra.Com's Answer #168431 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "What is the answer?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 1. Let $\"n\"$ be the first odd integer.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 2. Let $\"n%2B2\"$ and $\"n%2B4\"$ and be the next two consecutive integers.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 3. Let $\"n%2Bn%2B4=146\"$ since the sum of the least and greatest is 146.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 4. Solving the equation in Step 3 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: n=71.
Graphical form: Equation $\"n%2Bn%2B4=146\"$ was fully solved.
Text form: n+n+4=146 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+n%2Bn%2B4=146+%29\"$
For tutors: simplify_cartoon( n+n+4=146 )
If you have a website, here's a link to this solution.

\n" ); document.write( "

DETAILED EXPLANATION

\n" ); document.write( "

Look at $\"highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B4=146\"$ .
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 $\"highlight_green%28+%281%2B1%29%2An+%29%2B4=146\"$ .
\n" ); document.write( "

Look at $\"%28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B4=146\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+2+%29%29%2An%2B4=146\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+%28highlight_red%28+2+%29%29%2An+%29%2B4=146\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"highlight_green%28+2+%29%2An%2B4=146\"$ .
\n" ); document.write( "

Look at $\"2%2An%2B4=highlight_red%28+146+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-146+%29\"$
It becomes $\"2%2An%2B4-highlight_green%28+146+%29=0\"$ .
\n" ); document.write( "

Look at $\"2%2An%2Bhighlight_red%28+4+%29-highlight_red%28+146+%29=0\"$ .
Added fractions or integers together
It becomes $\"2%2An%2Bhighlight_green%28+-142+%29=0\"$ .
\n" ); document.write( "

Look at $\"2%2An%2Bhighlight_red%28+-142+%29=0\"$ .
Removed extra sign in front of $\"-142\"$
It becomes $\"2%2An-highlight_green%28+142+%29=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+2%2An-142+%29=0\"$ .
Solved linear equation $\"highlight_red%28+2%2An-142=0+%29\"$ equivalent to 2*n-142 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=71.

Universal Simplifier and Solver

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

\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "With n=71, then n+2=73 and n+4=75 where the sum of the least and largest number is 146. The sum is 71+73+75=219\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 8. ANSWER: The sum of the numbers is 219.\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 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( "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( "http://www.FreedomUniversity.TV\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );