Question

In the expression, Simon claims that 2x and -x are not like terms because -x does not have a coefficient. Is he correct? Explain your reasoning and then simplify the expression: 4m + 2x - x + 8.

a) Yes, Simon is correct.
b) No, Simon is not correct.
c) The expression cannot be simplified.
d) The expression is undefined.

Answer 1

Simon's claim that 2x and -x are not like terms is incorrect because -x has an implicit coefficient of -1. 2x and -x are like terms with the same variable 'x', and the expression 4m + 2x - x + 8 simplifies to 4m + x + 8.

Step-by-step explanation:

Simon claims that 2x and -x are not like terms because -x does not have a coefficient. This is incorrect; Simon's claim can be refuted by understanding that every variable term does have a coefficient, even if it's not explicitly written. For the term -x, the coefficient is actually -1. Therefore, 2x and -x are indeed like terms because they have the same variable part, 'x'. When simplifying the expression 4m + 2x - x + 8, you combine the like terms to get 4m + (2x - x) + 8, which simplifies further to 4m + x + 8.