Equivalent Expressions

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Equivalent expressions are the basically two equal expressions. It is denoted by the symbol ‘=’.  Expressions are said to be equivalent if and only if two expressions are same by substituting the values of variables. For example: - 3x + 4 = 2y +4, this expression is said t be equivalent if the value of x =2 and the value of y = 3. Let us clear our understanding by taking suitable examples.

Question 1:- If the following relation holds: - 2x+ 2 = 10 +2 then evaluate the value of x.

Solution 1:- Given 2x+2 = 10 +2

Step 1:- First let us solve Right hand side 2x + 2 = 12

Step 2:- Now we need to subtract w from both sides

             2x + 2-2 = 12-2

             2x = 10

Step 3:- To evaluate the value of x, now we need to divide by 2 in both sides of the equation

              2x/2 = 10 /2

Therefore,  x =5 is the required solution.
 
Question 2:- If 3x + 10 = 2y +5, then evaluate one value of x and y.

Solution 2:- Given expression is:  3x + 10 = 2y + 5

This problem needs to be solved by the hit and trial method, only thing here is we should focus that both the expressions are equivalent.

By hit and trial method, the value of x seems to be 5 and y seems to be 10

Check: - Left Hand Side = 3(5) + 10 = 25

Right Hand Side = 2(10) + 5 = 25

Since Left hand side = Right hand side

Therefore x = 5 and y = 10 is the required solution.

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