Question 151: -What does it mean for two algebraic expressions to be equivalent?
-What does it mean for a set of numbers to be a solution for an equation or inequality?
Answer by KMST(5484)   (Show Source):
You can put this solution on YOUR website! Two algebraic expressions are equivalent if they have the same value when the same value is used for each variable.
For example,
 is equivalent to  because
for every value of  both expressions result in the same number.
 and  are equivalent
because for each and every pair of  values,
the value for both expressions is the same.
 is not equivalent to 
because for  the first expression does not exist, while 
A set of numbers is the solution set for an equation or inequality if and only if
those are the only numbers make the equation of inequality true.
A number is a solution of an equation or inequality if
that number makes the equation or inequality true.
For example, the number  is a solution of  ,
because  ,
and the set of numbers in the interval (-1,1) is the solution set for ,
because all the numbers in that interval make true, and no other numbers are solutions.
and  are solutions for ,
because they make true.
The set {-1,1} is the solution set for
because and are the only solutions to .
and are solutions for ,
because they make true.
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