Answer: The required equation is ![\dfrac{1}{3}x+\dfrac{1}{2}x+2x=34.](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B3%7Dx%2B%5Cdfrac%7B1%7D%7B2%7Dx%2B2x%3D34.)
Step-by-step explanation: We are given to write the following statement as an equation :
"The sum of one-third of a number, one-half of a number and twice the number is thirty-four".
Let the number be represented by x.
Then, one-third of the number is
one-half of the number is
and twice the number is ![2x.](https://tex.z-dn.net/?f=2x.)
Therefore, as an equation, the given statement is written as:
![\dfrac{1}{3}x+\dfrac{1}{2}x+2x=34.](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B3%7Dx%2B%5Cdfrac%7B1%7D%7B2%7Dx%2B2x%3D34.)
Thus, the required equation is ![\dfrac{1}{3}x+\dfrac{1}{2}x+2x=34.](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B3%7Dx%2B%5Cdfrac%7B1%7D%7B2%7Dx%2B2x%3D34.)