Question

How do you solve $6+3t=8t-14$?

Answer 1

Hint: We separate the variables and the constants of the equation $6+3t=8t-14$. We apply the binary operation of addition and subtraction for both variables and constants. The solutions of the variables and the constants will be added at the end to get the final answer to equate with 0. Then we solve the linear equation to find the value of t.

Complete step by step answer:
The given equation $6+3t=8t-14$ is a linear equation of t. we need to simplify the equation by solving the variables and the constants separately.
All the terms in the equation of $6+3t=8t-14$ are either variable of t or a constant. We first separate the variables.
$\begin{align}
  & 6+3t=8t-14 \\
 & \Rightarrow 6+3t-8t+14=0 \\
\end{align}$
There are two such variables which are $3t$ and $8t$. The signs of the variables are both positive with coefficients being 3 and 8 respectively.
The binary operation between them is subtraction which gives us $3t-8t=-5t$.
Now we take the constants.
There are two such constants which are 6 and 14.
The binary operation between them is addition which gives us $6+14=20$.
The final solution becomes
$\begin{align}
  & 6+3t-8t+14=0 \\
 & \Rightarrow -5t+20=0 \\
\end{align}$.
Now we take the variable on one side and the constants on the other side. Then we divide both sides with 5.
\[\begin{align}
  & -5t+20=0 \\
 & \Rightarrow 5t=20 \\
 & \Rightarrow \dfrac{5t}{5}=\dfrac{20}{5} \\
 & \Rightarrow t=4 \\
\end{align}\]

The solution is $t=4$.

Note: We can verify the result of the equation $6+3t=8t-14$ by taking the value of t as $t=4$.
Therefore, the left-hand side of the equation becomes
$6+3t=6+3\times 4=6+12=18$.
the right-hand side of the equation becomes
$8t-14=8\times 4-14=32-14=18$
Thus, verified for the equation $6+3t=8t-14$ the solution is $t=4$.