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Algebra: A generalization of arithmetic inwhich letters representing numbers are combined according to therules of arithmetic. We looked at patterns of making letters and other shapes using matchsticks.
We learnt howto write thegeneral relation between the number ofmatchsticks required for repeating a given shape.
The number of times a given shape is repeated varies; it takes on values 1,2,3, It isa variable, denoted by some letter like n. A variable takes on different values, its value isnot fixed.
Thelength of a square canhave any value. It is a variable.
But the number of angles of a triangle has a fixed value 3.
It is nota variable. We may useany letter n,l, m, p,x, y, z,etc. to showa variable. A variable allows us toexpress relations inany practical situation. Variables are numbers, although their valueis not fixed.
We can dothe operations ofaddition, subtraction, multiplication and division on them just as in the case of fixed numbers.
Using different operations we can form expressions with variables like x –3, x +3, 2n, 5m,3 p ,2y + 3,3l – 5,etc. Variables allow us to express many common rules in both geometry and arithmetic in a general way.
For example, the rule thatthe sum of two numbers remains the sameif the order in which thenumbers are taken is reversed canbe expressed asa + b = b +a.
Here, thevariables a andb stand forany number, 1, 32, 1000– 7, – 20, etc. An equation isa condition ona variable.
It is expressed bysaying that anexpression with avariable is equal to a fixed number, e.g. x– 3 =10. An equation has twosides, LHS and RHS, between them is the equal (=) sign.
Solution of an Equation: The value ofthe variable inan equation whichsatisfies the equation. For getting thesolution of anequation, one method is the trial and error method.
In this method, we give somevalue to thevariable and checkwhether it satisfies the equation.
We goon giving thisway different values to the variable until we findthe right which satisfies the equation. The LHS of an equation is equal to its RHS only for a definite value of the variable in the equation.
We say that this definite value of the variable satisfies the equation.
This value itself is called thesolution of theequation. For getting the solution of an equation, one method is the trial and error method.
In this method, we give some value to the variable and check whether it satisfies the equation.
We goon giving thisway different values to the variable` until we find the right value which satisfies the equation.
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