Question

Solve the following equation and find the value of t: $\dfrac{\left( 3t-2 \right)}{4}-\dfrac{\left( 2t+3 \right)}{3}=\dfrac{2}{3}-t$

Answer 1

Hint: In the above given question we have been asked to solve the given algebraic equation $\dfrac{\left( 3t-2 \right)}{4}-\dfrac{\left( 2t+3 \right)}{3}=\dfrac{2}{3}-t$ . For doing that we will simplify the given expression by performing some simple arithmetic operations like addition and transform some of the terms from left hand side to right hand side.

Complete step-by-step solution:
Now considering from the question we have been asked to solve the given algebraic equation $\dfrac{\left( 3t-2 \right)}{4}-\dfrac{\left( 2t+3 \right)}{3}=\dfrac{2}{3}-t$ .
Firstly we will transfer $-t$ from right hand side to left hand side in order to arrange all the terms containing the variable $t$ on the same side by doing that we will have $\Rightarrow \dfrac{\left( 3t-2 \right)}{4}-\dfrac{\left( 2t+3 \right)}{3}+t=\dfrac{2}{3}$ .
Now we will simplify the equation on the left hand side and make it having a single equal denominator after doing that we will have
$\begin{align}
  & \Rightarrow \dfrac{3\left( 3t-2 \right)}{4\times 3}-\dfrac{4\left( 2t+3 \right)}{3\times 4}+\dfrac{12t}{12}=\dfrac{2}{3} \\
 & \Rightarrow \dfrac{9t-6-8t-12+12t}{12}=\dfrac{2}{3} \\
\end{align}$
Now we will further simplify this expression after doing that we will have $\begin{align}
  & \Rightarrow \dfrac{13t-18}{12}=\dfrac{2}{3} \\
 & \Rightarrow 13t-18=\dfrac{2}{3}\left( 12 \right) \\
\end{align}$
By further simplifying this expression we will have
$\begin{align}
  & \Rightarrow 13t=8+18 \\
 & \Rightarrow t=\dfrac{26}{13} \\
 & \Rightarrow t=2 \\
\end{align}$
Therefore we can conclude that the solution of the given algebraic equation $\dfrac{\left( 3t-2 \right)}{4}-\dfrac{\left( 2t+3 \right)}{3}=\dfrac{2}{3}-t$ is $t=2$.

Note: While answering questions of this type we should be very careful during the preformation of calculations in between the steps. This is a very simple and easy question and can be answered in a short span of time. Very few mistakes are possible in questions of this type. Someone can make a mistake during calculation and consider it as $\begin{align}
  & \dfrac{\left( 3t-2 \right)}{4}-\dfrac{\left( 2t+3 \right)}{3}=\dfrac{2}{3}-t \\
 & \Rightarrow 13t=8+18 \\
 & \Rightarrow t=\dfrac{26}{13} \\
 & \Rightarrow t=3 \\
\end{align}$
which will lead them to end up having a wrong conclusion.