Equivalent Expressions / Equivalent Equations

Date: 07/27/97 at 13:12:25
From: Anonymous
Subject: Equivalent expressions and equivalent equations

Dr. Math,

Could you please explain the difference between equivalent expressions 
and equivalent equations?

Thank you,
Linda

Date: 07/29/97 at 11:33:50
From: Doctor Rob
Subject: Re: Equivalent expressions and equivalent equations

Good question!  This is often a source of confusion to students.

Equivalent expressions have the same value for every possible value of
the variables they include.  5*(x-4) and 5*x - 20 are equivalent
expressions because no matter what the value of x, they are equal in 
value.

Equivalent equations are ones such that the truth of one implies and
is implied by the truth of the other.  (y-2)^2 = 0 and y = 2 are
equivalent equations, even though the expressions y and (y-2)^2 are
not equivalent expressions.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/