Question

How do you solve $ - 23 = x + 8$?

Answer 1

Hint: Here, we are given a linear equation in one variable. A linear equation in one variable is an equation of the standard form,
$ax + b = 0$ , where $a,b$ are constants.
 Such an equation has one and only one solution, which is given by,
$x = \dfrac{{ - b}}{a}$

Complete step-by-step answer:
We are given an equation, $ - 23 = x + 8$ .
Let us first rearrange this into standard form.
For that let us add 23 on both sides of the equation as shown below,
$ - 23 + 23 = x + 8 + 23$
(This is possible since addition or subtraction of the same constants on both sides of an equality sign does not change the equation.)
$ \Rightarrow 0 = x + 31$
$ \Rightarrow x + 31 = 0$
Comparing this to the standard equation $ax + b = 0$ ,we have ,
$a = 1$ and
$b = 31$
Therefore, the only one solution to this linear equation in single variable $x$ is,
$x = \dfrac{{ - b}}{a}$
    $ = \dfrac{{ - 31}}{1}$
$ \Rightarrow x = - 31$.
That is the solution to the given equation, $ - 23 = x + 8$ , is given by $x = - 31$

Additional information:
A quadratic equation of a single variable is of order two and hence it can have at most two solutions.
Similarly, with an $n^{th}$ degree equation in a single variable, the maximum number of possible solutions it can have is $n$.

Note: One must be careful in deriving the standard equation, without making mistakes in signs of numbers. As the linear equation in a single variable is an equation of order one and hence one solution.