Question

A math class is having a discussion on how to determine if the expressions 4x-x+5 and 8-3x-3 are equivalent using substitution. The class has suggested four different methods.

Which describes the correct method?
1) Both expressions should be evaluated with one value. If the final values of the expressions are both positive, then the two expressions must be equivalent.
2)Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.
3)Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.
4)Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

Answer 1

Okay. In my opinion, all the class has to do is simplify the expressions and compare. But they want to substitute instead.

Well then.

First, let's notice that these are linear expressions, meaning that if they are equivalent then all their values match up.

Number 1 is not a good one. Just because they're both positive doesn't mean anything; they have to be the same.

This also eliminates 3.

Number 2 is a good one, but it's not as reliable. If, for instance, the two expressions are not equivalent and you get lucky enough to pick that one value they intersect at (or have in common), then you'd be wrong when you say they are equivalent.

Number 4 makes the most sense because if both expressions are equivalent, then every value matches up. If not, then only one will. So having two values to substitute will most definitely answer the class question.

Hope this helps, let me know if I messed up! ;)

Answer 2

Answer:

the last one

Step-by-step explanation:

4.) Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.