What are equivalent expressions?

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.

50x5=$250

step-by-step explanation: