Question

Solve \[3y + \dfrac{5}{2} = \dfrac{{19}}{3} - 2y\]

Answer 1

Hint: The given equation is a one variable and one equation form, to solve this equation you have to shift all the variables to the left hand side of the equation whereas constants to the right hand side of the equation then simplify it and after simplifying the equation, divide both side of the equation with coefficient of the variable to get the required solution.

Complete step by step answer:
In order to solve the given one variable one equation, that is \[3y + \dfrac{5}{2} = \dfrac{{19}}{3} - 2y\], we will go through the following steps:
Step I: Here we will shift all the variables to the left hand side of the equation with help of arithmetic operations, so if we add $2y$ to both sides of the equation then variable at R.H.S. will get eliminated as follows
\[
   \Rightarrow 3y + \dfrac{5}{2} + 2y = \dfrac{{19}}{3} - 2y + 2y \\
   \Rightarrow 5y + \dfrac{5}{2} = \dfrac{{19}}{3} \\
 \]
Step II: In this step we will eliminate the constant present at the L.H.S. by subtracting \[\dfrac{5}{2}\] both sides and then we will simplify it, we will get
\[
   \Rightarrow 5y + \dfrac{5}{2} - \dfrac{5}{2} = \dfrac{{19}}{3} - \dfrac{5}{2} \\
   \Rightarrow 5y = \dfrac{{19}}{3} - \dfrac{5}{2} \\
   \Rightarrow 5y = \dfrac{{38 - 15}}{6} \\
   \Rightarrow 5y = \dfrac{{23}}{6} \\
 \]
Step III: In this step we will divide both side of the equation with the coefficient of the variable, which is $5$ in the above equation, so dividing both sides of the equation with $5$ we will get
\[
   \Rightarrow \dfrac{{5y}}{5} = \dfrac{{23}}{{6 \times 5}} \\
   \Rightarrow y = \dfrac{{23}}{{30}} \\
 \]

Therefore \[y = \dfrac{{23}}{{30}}\] is the solution of the given equation.

Note: When you solve this type of more questions and get the solution in fraction as in this question, then must check if the fraction is in its simplified form or not, also check for the proper and improper fraction and if found improper one then make it proper.