Question

Brianna’s teacher asks her which of these three expressions are equivalent to each other.

Expression A:
9x−3x−4
Expression B:
12x−4
Expression C:
5x+x−4

Brianna says that all three expressions are equivalent because the value of each one is −4 when x 0.
Brianna’s thinking is incorrect.
Identify the error in Brianna’s thinking.
Determine which of the three expressions are equivalent.
Explain or show your process in determining which expressions are equivalent.

Answer 1

The error in Brianna's thinking is that she only tested the expressions when x is equal to 0. However, to determine if the expressions are equivalent, we need to test them for all possible values of x.

Expression A: 9x - 3x - 4 = 6x - 4
Expression B: 12x - 4
Expression C: 5x + x - 4 = 6x - 4

Expressions A and C are equivalent because they both simplify to 6x - 4. Expression B is not equivalent to either of the other expressions because it cannot be simplified any further.

Hope this helps