SOLUTION: The sum of the integer and twice its reciprocal is 11/3. Find the integer.

Algebra ->  Equations -> SOLUTION: The sum of the integer and twice its reciprocal is 11/3. Find the integer.      Log On


   

Question 369736: The sum of the integer and twice its reciprocal is 11/3. Find the integer.
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
+x+%2B+2%2Fx+=+11%2F3+
multiply both sides by 3x
3x%5E2%2B6+=+11x
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=3,x=0.666666666666667.
  • Graphical form: Equation 3x%5E2%2B6=11x was fully solved.
  • Text form: 3x^2+6=11x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3x%5E2%2B6=11x+%29
    For tutors: simplify_cartoon( 3x^2+6=11x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2Ax%5E2%2B6=highlight_red%28+11%2Ax+%29.
Moved these terms to the left highlight_green%28+-11%2Ax+%29
It becomes 3%2Ax%5E2%2B6-highlight_green%28+11%2Ax+%29=0.
Look at 3%2Ax%5E2%2Bhighlight_red%28+6+%29-11%2Ax=0.
Moved 6 to the right of expression
It becomes 3%2Ax%5E2-11%2Ax%2Bhighlight_green%28+6+%29=0.
Look at highlight_red%28+3%2Ax%5E2-11%2Ax%2B6+%29=0.
Equation highlight_red%28+3%2Ax%5E2-11%2Ax%2B6=0+%29 is a quadratic equation: 3*x^2-11*x+6 =0, and has solutions 3,0.666666666666667
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=3,x=0.666666666666667.

Universal Simplifier and Solver


Done!


x=3 is your answer, as the other answer is not integer.