Question

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

Answer: 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.

Step-by-step explanation:

4x - x + 5 = 8 - 3x - 3

Combine like terms

4x - x + 5 = 5 - 3x

Subtract x from 4x

3x + 5 = 5 - 3x

Add -3x to both sides

6x + 5 = 5

Subtract 5 from each side

6x = 0

Divide by 6

x = 0

Put 0 into the equation

4(0) - 0 + 5 = 8 - 3(0) - 3

Multiply

0 - 0 + 5 = 8 - 0 - 3

Subtract

5 = 5