A teacher asked the students to write the following statements :

(i) Twice of x plus four

(ii) Three time x minus 7

Students responded as 2x + 4 and 3x - 7, while the teacher was expecting 2(x + 4) and 3 (x - 7). The above mistakes have occurred due to

The mistake occurred due to the ambiguous language used by the teacher, which led students to interpret the instructions differently than intended.

Key Points

• The students' responses indicate that they interpreted the teacher's instructions differently than intended. This misunderstanding likely stems from the way the instructions were phrased.
• The teacher's language might have led the students to think that the operations should be performed directly on "x" before adding or subtracting the constants. 
• If the teacher had said, "Twice the sum of x and four" for the first statement, and "Three times the difference of x and seven" for the second statement, the students would more likely be understood to use the expressions 2(x+4) and 3(x−7), respectively.

Hence, we can conclude that the above mistakes have occurred due to the language used by a teacher.