Question

Explain why 2+x and x+3 are equivalent

Answer 1

Check whether the two expressions 2x+3y2x+3y and 2y+3x2y+3x equivalent.

The first expression is the sum of 2x2x 's and 3y3y 's whereas the second one is the sum of 3x3x 's and 2y2y 's.

Let us evaluate the expressions for some values of xx and yy . Take x=0x=0 and y=1y=1 .

2(0)+3(1)=0+3=32(1)+3(0)=2+0=22(0)+3(1)=0+3=32(1)+3(0)=2+0=2

So, there is at least one pair of values of the variables for which the two expressions are not the same.