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.

Explain the error in Brianna’s thinking

Answer 1

Expression A & Expression C are equivalent

Explanation:

●In Expression A :-

9x - 3x - 4

=> 6x - 4 ( Substracting the like terms )

● In Expression C :-

5x + x - 4

=> 6x - 4 ( Adding like terms )

● In Expression B

12x - 4

Comparing all the expressions , we find both expression A & C have 5x - 4 as eqn. So they are equivalent.

Eqns are known as equivalent only when the final result will be equal after putting 'n' number of values in place of the variable. For example ,

expression A & C are equivalent. If we gonna take x = 1 , then the final result will be 6×1 - 4 = 2. Here we find that after putting x=1 in the expressions , the final result is equal in both the expressions & that is 2.

So the mistake of Brianna was her wrong assumption about equivalent expression.