Final answer:
The expressions 7x+4-x-2 and 6x+2 are equivalent by combining like terms and using the Commutative and Associative Properties of Addition. Simplifying the terms and grouping them correctly results in the simplified expression, which can be verified by substituting values for x.
Step-by-step explanation:
The expressions 7x+4-x-2 and 6x+2 are proved to be equivalent by using the properties of algebra. To show the equivalence, we first combine like terms by adding together the x's and the constants separately. The expression simplifies to 7x - x + 4 - 2, which simplifies further to 6x + 2 by using the Combination of Like Terms.
During this process, the properties used include the Commutative Property of Addition, which allows us to rearrange the terms, and the Associative Property of Addition, which allows us to group terms in any way to aid in simplification. By using these properties, the expression smoothly simplifies to its equivalent form.
To check if the answer is reasonable, one can substitute a value for x into both expressions to see if they yield the same result, in accordance with the steps for verifying the solution of algebraic expressions.