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Question

Question: How do you solve \( - 23 = x + 8\)?...

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

Explanation

Solution

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=0ax + b = 0 , where a,ba,b are constants.
Such an equation has one and only one solution, which is given by,
x=bax = \dfrac{{ - b}}{a}

Complete step-by-step answer:
We are given an equation, 23=x+8 - 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- 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.)
0=x+31\Rightarrow 0 = x + 31
x+31=0\Rightarrow x + 31 = 0
Comparing this to the standard equation ax+b=0ax + b = 0 ,we have ,
a=1a = 1 and
b=31b = 31
Therefore, the only one solution to this linear equation in single variable xx is,
x=bax = \dfrac{{ - b}}{a}
=311= \dfrac{{ - 31}}{1}
x=31\Rightarrow x = - 31.
That is the solution to the given equation, 23=x+8 - 23 = x + 8 , is given by x=31x = - 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 nthn^{th} degree equation in a single variable, the maximum number of possible solutions it can have is nn.

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.