Q: What is the definition of an equivalent variable expressions?

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Yes. That is the definition of an algebraic expression.

That means that the two expressions represent the same number.

You can use them to find a variable. Lets say you have two equivalent expressions with the same variable... x + 2x - 42 = 0 2x - 28 = 0 If you combine these equivalent expressions you ahve... x + 2x - 42 = 2x - 28 In all of the expressions you have x = 7 There are also other applications but its confusing to explain.

They are identical or equivalent.

choosing a variable to represent one of the unspecified numbers in a problem and using it to write expressions for the other unspecified numbers in the problem.

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Two expressions are "equivalent" if they have the same result for any values of the variable or variables.

Yes. That is the definition of an algebraic expression.

That means that the two expressions represent the same number.

equivalent equations

You can use them to find a variable. Lets say you have two equivalent expressions with the same variable... x + 2x - 42 = 0 2x - 28 = 0 If you combine these equivalent expressions you ahve... x + 2x - 42 = 2x - 28 In all of the expressions you have x = 7 There are also other applications but its confusing to explain.

They are identical or equivalent.

two expressions that have the same value for all allowable replacements are called equivalent.

choosing a variable to represent one of the unspecified numbers in a problem and using it to write expressions for the other unspecified numbers in the problem.

Expressions never have equality signs

Lots of expressions are equivalent to it. But for a start, you may want to simplify it, by combining like terms - i.e., add the terms with the variable "w", and separately add the terms without a variable.

It means that two expressions represent the same number; for example, 5 is equivalent to 3 + 2. If there are variables in the expression, it means that the two expressions will evaluate to the same number, for any value assigned to the variable or variables. For example, for any value of x, 2x is the same as x + x; therefore, the two are equivalent.

An expression with a variable.