Question

How do you solve this? \[\dfrac{2}{3}+\dfrac{5}{6}=\dfrac{x}{2}\]

Answer 1

Hint: These types of problems are very straight forward and are simple demonstrations of linear equations. For these types of problems, we first of all need to perform fraction addition, which is done by taking the Least Common Multiple of the denominators of the two fractions and then equating with the unknown parameter. We then solve, and find the value of the unknown parameter.

Complete step-by-step solution:
Now, we start off with the solution of the problem. We first of all perform fraction addition. In doing so we need to find the least common multiple (L.C.M) of the denominators of the fractions in the left hand side of the given equation. Thus, the L.C.M of \[3\] and \[6\] is \[6\]. Now taking the denominator as \[6\], we write the right hand side as,
\[=\dfrac{\left( 2\times 2 \right)+5}{6}\]
Now, doing simple linear multiplication followed by linear summation of the integers, we get,
\[\begin{align}
  & =\dfrac{4+5}{6} \\
 & =\dfrac{9}{6} \\
\end{align}\]
Now, reducing the above fraction to its simplest form we get (Taking \[3\] common from both the numerator and the denominator and then cancelling it) ,
\[=\dfrac{3}{2}\]
Now we equate this left hand side of the equation to the right hand side and we write,
\[\dfrac{3}{2}=\dfrac{x}{2}\]
Now, cross-multiplying both the sides of the equation, we get,
\[\Rightarrow 2x=6\]
Now, evaluating for the value of \[x\], we get,
\[\Rightarrow x=3\]
Thus the answer to our problem is \[x=3\] .

Note: These types of problems can also be solved using another method. We can do it using the graphical method. In this method, we first find out the linear equation in terms of the unknown parameter. We then plot this line in the coordinate plane, and find out its intersection point with the line \[y=0\] . For solving, we must also remember the law of addition of fractions.