Solving Equations
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Solving Equations
Solving Equations is the process of finding the values of the variables or
unknown quantities that are satisfied by the condition defined in the equation.
An equation is described as the combination of the variables and the values,
and these equations are solved by using three different ways: with the help of
algebra, by graphs, by using the concept of equivalence. There are several
equations that define the different types of equations as:
a  2 = 4 or
2 p  4 = 16 or
3 s  8 = 5 s  6 or
3 / 4 a + 5 / 6 = 5 a  125 / 3 or
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2 (3 p  7) + 4 (3 p + 2) = 6 (5 p + 9) + 3 or
6 a  7/4 + 3 a  5/7 = 5 a + 78/28 etc.
The above equations have variables like a, x, p or s. etc and the constant
values that are joined with each other using some operations like addition /
subtraction / multiplication / division.
These types of equations are known as linear equations and we solve
equations as follows: If we take equations a + b = 2 a  1 and a = b + 1 then the
value of the variable a is calculated by putting the value b + 1 in place of a, so
the equation is written as ( b + 1 ) + b = 2 ( b + 1 )  1.
Then in the equation only variable b is unknown and the value of b is equal to 0
thus we get the value of a that is equal to 1. So we can write it as (a, b) = (1, 0).
The process to solve equation that contains radicals is shows below:
(a  8) 1 / 2 = 3 is a radical equation and is solved by taking the square of both
sides of equality sign as ((a  8) 1 / 2 ) 2 = ( 3 ) 2
a  8 = 9
And a = 9 + 8
a = 17
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(It should be remembered that we never take the square root of negative
number). We can take some examples of solving equations that have the
absolute values:
 2 a  1  = 5 is an equation of absolute value that can be solved in some steps.
Isolate the absolute value as: 2 a  1 = 5  (1)
Or 2 a  1 =  5  (2)
Now solve equation (1): 2 a  1 = 5
2 a= 6
a = 3
Solve equation (2): 2 a  1 =  5
2 a =  4
a = 2
There are two solutions 3 and 2. Put them into the actual equation and find the
answer as
 2 a  1  = 5
 2. 3  1  = 5
 6  1  = 5
5 = 5 so the result is 5.
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