The general form of linear equation consisting of one variable can be written as
where
is the only variable and
are real numbers.
Let’s suppose I want to find value of
from the equation
It means that I will have to eliminate b from the left hand side and also have to eliminate a from the left hand side. Doing so, I will be left with just
on the left hand side and whatever would be present on the right hand side at that time would be the value of
(Solution of equation).
To eliminate a and b from
, we do the following:
(Step 1) Subtract b from both the sides, we get
(Step 2) Now divide both the sides by a, we get
So, this is the value of
or the solution of given linear equation.
Now, take an example. I have linear equation:
What is the solution of this linear equation?
To solve it, we just need to follow the same process. I will eliminate 2 and -5 from the left hand side.
(Step 1) Adding 5 to both the sides, we get
(Step 2) Dividing both the sides by 2, we get
(This is the solution)
Let’s do 2nd example now, I have equation:
(Step 1) Adding 6 to both sides, we get
(Step 2) Dividing both sides by -2, we get
(This is the solution)
Take 3rd example now which is relatively more complex. I have equation:
(Step 1) Subtracting
from both the sides, we get
(Step 2) Multiplying both the sides by
, we get
(This is the solution)
Take 4th example now, which is relatively easier than 3rd example. It will help you in understanding 3rd example if you could not understand it. Let’s suppose, I have equation:
(Step 1) Subtracting 7 from both the sides, we get
(Step 2) Multiplying both the sides by 3, we get
(This is the solution)
Equations can be more complex than the examples that we just covered but the overall process remains the same. Let’s consider equation:
(Step 1) Subtracting 4 from both the sides, we get
Note that we have two terms here consisting of
. So, we have to combine them in order to find solution.
(Step 2) Subtracting
from both the sides, we get
(At this step, you should know how to add or subtract fractions)
(Step 3) Multiplying both the sides by 4, we get
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