Equations

 

Objective

 

This Topic gives an overview of;

 

  • Algebraic Equation
  • Solution of an Equation
  • Examples using Equations

 

Algebraic Equation

 

A mathematical statement that indicates that the value of the LHS is equal to the value of the RHS is called an Equation.

 

Let us recall the matchstick pattern of the letter L. The number of matchsticks required for different number of Ls formed was given as 2 X n or 2n.

 

Here in this case, n is taken to be the number of Ls formed. Now for an example a student need to find out the number of Ls formed, knowing that the number of matchsticks needed is 10.

 

Hence we can write it as, 2n=10. 

 

Here n is unknown. The value of “n” must be such that it should satisfy the condition above. This condition is called Algebraic equation. Hence that any equation like the above, is a condition on a variable .It is satisfied only for a definite value of the variable.

 

An equation has an equal sign (=) between its two sides. The equation says that the value of the left hand side (LHS) is equal to the value of the right hand side (RHS). If the LHS is not equal to the RHS, we do not get an equation. So hence to find out whether the given equation is an Algebraic Equation or not we have to check two things, an equation must have an equal sign (=) and a variable.


Solution of an Equation

 

The value of the variable in an equation which satisfies the equation is called a Solution to the Equation. So for example we take the equation 2n=10, If n = 1, the number of matchsticks is 2. Clearly, the condition is not satisfied, because 2 is not 10. We go on checking.

 

 

We find that only if n = 5, the condition, i.e. the equation 2n = 10 is satisfied. For any value of n other than 5, the equation is not satisfied.

 

In finding the solution to the equation 2n = 10, we prepared a table for various values of n and from the table, we picked up the value of n which was the solution to the equation. This method is called a Trial and Error method. It is not a direct and practical way of finding solution.


Examples using Equations


Let us take the equation x – 3 = 11.


This equation is satisfied by x = 14, because for x = 14,

 LHS of the equation = 14 – 3 = 11 = RHS.

 

Thus, x = 14 is a solution to the equation. We will find this by just adding 11 and 3. Let us look at other examples.

 

  • X – 3 = 11, X = 11 + 3, so hence X = 14.
  • X + 10 = 30, X= 30 – 10 , so hence X = 20
  • 2N=10, N=10/2, so hence N=5
  • M/5=4, M=5 X 4, so hence M=20.

 

 Here is a table which displays more of examples. 

 

 

Summary

 

  • An equation is a condition on a variable. It is expressed by saying that an expression with a variable is equal to a fixed number, e.g. x – 3 = 10.
  • An equation has two sides, LHS and RHS, between them is the equal (=) sign.
  • 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 the solution of the equation.
  • 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 go on giving this way different value to the variable until we find the right value which satisfies the equation.

 

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