Question

How do you solve $5t - 26 = 18t$?

Answer 1

Hint: Here we are given a simple equation and asked to solve for the variable $t$. We need to rearrange or alter the given equation. Firstly, we have to separate the variables from the constant terms (numbers) by transferring it to the other side. We need to make sure that terms containing $t$ as variables must be on one side of the equation and the constant terms must be on the other side. Then we solve the given problem by using the basic mathematical operations and transferring methods to obtain the required solution.

Complete step by step solution:
Here we have given the equation $5t - 26 = 18t$ ……(1)
We are asked to solve the above expression given in the equation (1) to obtain the value for the unknown variable $t$.
Now we solve for the variable $t$.
Remember that we have to keep the terms containing the variable $t$ in one side and all the other terms which are constant to the other side of the equation.
In this problem we keep terms with $t$ in the L.H.S. and constants in the R.H.S. of the equation.
Now subtracting $5t$ from both sides of the equation (1), we get,
$ \Rightarrow 5t - 26 - 5t = 18t - 5t$
Rearranging the terms we get,
$ \Rightarrow 5t - 5t - 26 = 18t - 5t$
Combining the like terms, $5t - 5t = 0$
Combining the like terms, $18t - 5t = 13t$
Hence we get,
$ \Rightarrow 0 - 26 = 13t$
This can also be written as,
$ \Rightarrow 13t = 0 - 26$
$ \Rightarrow 13t = - 26$
Now dividing throughout the equation by 13 we get,
$ \Rightarrow \dfrac{{13t}}{{13}} = - \dfrac{{26}}{{13}}$
Simplifying this we get,
$ \Rightarrow t = - 2$
Hence the solution for the equation $5t - 26 = 18t$ is given by $t = - 2$.
Now to verify whether the obtained value of $t$ satisfies the given equation $5t - 26 = 18t$, for this we substitute $t = - 2$ in the equation and we must obtain L.H.S. is equal to R.H.S.
Substituting $t = - 2$ in $5t - 26 = 18t$ we get,
$5(- 2) - 26 = 18( - 2)$
$ \Rightarrow - 10 - 26 = - 36$
$ \Rightarrow - 36 = - 36$
Hence L.H.S. is equal to R.H.S.

Therefore the required value of $t$ is, $t = - 2$.

Note: If the question is given in the form of MCQ , we can directly apply the values of $t$ mentioned. If the equation satisfies the value of $t$, then it is the required value for the given problem.
We need to be careful while taking the terms to the other side. When transferring any variable or number to the other side, the sign of the same will be changed to its opposite sign.
It is important to know the following basic facts.
An equation remains unchanged or undisturbed if it satisfies the following conditions.
(1) If L.H.S. and R.H.S. are interchanged.
(2) If the same number is added on both sides of the equation.
(3) If the same number is subtracted on both sides of the equation.
(4) When both L.H.S. and R.H.S. are multiplied by the same number.
(5) When both L.H.S. and R.H.S. are divided by the same number.