Answer:
Consider the expressions 32+1 and 5×2 . Both are equal to 10 . That is, they are equivalent expressions.
Now let us consider some expressions that include variables, say 5x+2 .
The expression can be rewritten as 5x+2=x+x+x+x+x+1+1 .
We can re-group the right side of the equation to 2x+3x+1+1 or x+4x+2 or some other combination. All these expressions have the same value, whenever the same value is substituted for x . That is, they are equivalent expressions.
Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Example 1:
Are the two expressions 2y+5y−5+8 and 7y+3 equivalent? Explain your answer.
Combine the like terms of the first expression.
Here, the terms 2y and 5y are like terms. So, add their coefficients. 2y+5y=7y .
Also, −5 and 8 can be combined to get 3 .
Thus, 2y+5y−5+8=7y+3 .
Therefore, the two expressions are equivalent.
Example 2:
Are the two expressions 6(2a+b) and 12a+6b equivalent? Explain your answer.
Use the Distributive Law to expand the first expression.
6(2a+b)=6×2a+6×b =12a+6b
Therefore, the two expressions are equivalent.
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