Question

How to make $x$ the subject?
$A - x = \dfrac{{xr}}{t}$

Answer 1

Hint:
Here, we are required to make \[x\] the subject. Thus, we will solve the given equation such that we are able to take \[x\] common which could be further rearranged. We will then solve it in such a way that it gets ‘shifted’ or ‘moved’ to the LHS and all other terms remain in the RHS. Hence, making \[x\] the subject of the equation.

Complete step by step solution:
We need to make $x$ the subject, it means to write all the terms in terms of $x$.
Here, we will use rearranging formulae.
According to the rearranging formulae, we can add, subtract, multiply and divide by anything, as long as we do the same thing to both the sides of the equals sign and rearrange it. With the help of this rearranging formula, we can rearrange the given equation and write it further with the $x$ terms on one side and other terms on the other side of the equals to sign.
Thus, given expression is:
$A - x = \dfrac{{xr}}{t}$
Multiplying \[t\] on both the sides, we get
$ \Rightarrow At - xt = xr$
Adding $xt$ on both sides, we get
$ \Rightarrow At = xr + xt$
Taking $x$ common from RHS, we get
$ \Rightarrow At = x\left( {r + t} \right)$
Dividing both sides by $\left( {r + t} \right)$, we get
$ \Rightarrow x = \dfrac{{At}}{{\left( {r + t} \right)}}$
Hence, this is the required answer where $x$ is the subject.

Note:
In mathematics, “to make $x$ the subject” means that we are required to make an equation such that all the terms having $x$ are on the left hand side. Also, it shows that $x$ is an independent variable because substituting any value in $x$ will change the relationship in the RHS. Thus, these questions are solved just by rearranging the given equation and taking all the terms with $x$ on the LHS. The given equation is a linear equation because the highest degree of the variable is 1.