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Equation:
An equation is a mathematical statement that has two expressions separated by an equal sign. The expression on the left sign of the equal sign has the same value as the expression on the right side.
One or both of the expressions may contain variables. Solving an equation means manipulating the expressions and finding the value of the variables for which it is true.
For Example
2X+10=20 is an equation
We can solve it to find the value of X
:. 2X = 20-10 = 10
Or, X= 10/2 = 5
:. X = 5 is the solution to this equation.
Solving equation:
The basic principle that you must adhere to in solving any equation is that you can manipulate it in anyway, so long as you do the same thing to both sides. For example, you may add/ subtract the same number from both sides; multiply or divide each side by the same numbers (except 0;); square each side; take the square root of each side (if the quantities are positive); or take the reciprocal of each side.
e.g. wile solving the last example we followed the following steps.
2X+10=20
Step: 1: Subtract 10 from both sides.
2X+10-10=20-10=10
Step:2: Divide both sides by 2
2X/2 = 10/2
Or X = 5
So, the solution is X=5.
Solving equation is an art. There are so many types of equations & so many ways of slaving them that there is no point trying to list them. The more you practice equation solving, the better you can.
The next equation solving will show a few most commonly used steps.
1/2X+3(X-2) = 2(X+1)+1
Step:1: Get rid of fractions and decimals by multiplying both sides by the lowest common denominator (LCD)
X+6(X-2) = 4(X+1)+2
Step:2: Now remove all the parenthesis.
X+6X-12 =4X +4+2
Step:3: Combine like terms on each side.
7X-12=4X+6
Step:4: By adding or subtracting get all the variables on one side & all the plain numbers on the other side.
:. 7X-4X = 12+6
:. 3X=18
Step:5: Divide both sides by the co-efficient of the variables.
3X/3=18/3
Or, X=6
Answer: X=6
Sometimes you are asked to solve one variable in terms of other variables. In such cases we treat all of the others as if they were numbers and then apply steps similar to those discussed in the previous examples.
e.g. if a = 3b-c, what is the value of (b) in terms of (a) & (c)?
a=3b-c
Step:1: Add c to both sides.
a+c=3b
Step:2: Divide both side by 3
b=(a+c)/3 (Answer)
Very ofter, solving the equation is not the quickest way to answer the question. consider the following example.
If 2X-5=98 then what is the value of 2X+5?
Here you have not been asked to find out the value of X. Though it is possible to calculate 2X+5 from the value of X, there is an easier way. Note that
(2X+5)-(2X-5) =10
So, adding 10 to both sides of the given equation, we have
2X-5+10=98+10
:. 2X+5 = 108 (Answer)
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