SOLUTION: The sum of a number and two is three more than twice the same number

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Question 223673: The sum of a number and two is three more than twice the same number
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of a number and two is three more than twice the same number.

Step 1. Let n be the number

Step 2. Let n+2 be the sum of a number and 2.

Step 3. Let 2n+3 be three more than twice the number.

Step 4. Then n+2=2n+3 since the sum of a number and two is three more than twice the same number.

Step 5. Solving the equation in Step 4 yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: n=-1.
  • Graphical form: Equation n%2B2=2n%2B3 was fully solved.
  • Text form: n+2=2n+3 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2B2=2n%2B3+%29
    For tutors: simplify_cartoon( n+2=2n+3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at n%2B2=highlight_red%28+2%2An%2B3+%29.
Moved these terms to the left highlight_green%28+-2%2An+%29,highlight_green%28+-3+%29
It becomes n%2B2-highlight_green%28+2%2An+%29-highlight_green%28+3+%29=0.
Look at n%2Bhighlight_red%28+2+%29-2%2An-highlight_red%28+3+%29=0.
Added fractions or integers together
It becomes n%2Bhighlight_green%28+-1+%29-2%2An=0.
Look at n%2Bhighlight_red%28+-1+%29-2%2An=0.
Moved -1 to the right of expression
It becomes n-2%2An%2Bhighlight_green%28+-1+%29=0.
Look at n-2%2An%2Bhighlight_red%28+-1+%29=0.
Removed extra sign in front of -1
It becomes n-2%2An-highlight_green%28+1+%29=0.
Look at highlight_red%28+n+%29-highlight_red%28+2%2An+%29-1=0.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+-2%2An+%29 replacing them with highlight_green%28+%281-2%29%2An+%29
It becomes highlight_green%28+%281-2%29%2An+%29-1=0.
Look at %28highlight_red%28+1+%29-highlight_red%28+2+%29%29%2An-1=0.
Added fractions or integers together
It becomes %28highlight_green%28+-1+%29%29%2An-1=0.
Look at %28highlight_red%28+-1+%29%29%2An-1=0.
Removed extra sign in front of -1
It becomes %28-highlight_green%28+1+%29%29%2An-1=0.
Look at highlight_red%28+%28-highlight_red%28+1+%29%29%2An+%29-1=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes -highlight_green%28+1+%29%2An-1=0.
Look at -highlight_red%28+1+%29%2An-1=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -n-1=0.
Look at highlight_red%28+-n-1+%29=0.
Solved linear equation highlight_red%28+-n-1=0+%29 equivalent to -n-1 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=-1.

Universal Simplifier and Solver


Done!



Step 6. ANSWER: The number is -1.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J