Question
Question: How do you solve \( - 23 = x + 8\)?...
How do you solve −23=x+8?
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=0 , where a,b are constants.
Such an equation has one and only one solution, which is given by,
x=a−b
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.)
⇒0=x+31
⇒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=a−b
=1−31
⇒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 nth 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.