Question

A student consistently simplifies algebraic expressions as shown below. 2x+3x+5=20 10x=20 x=2 This work provides the most direct evidence that this student does not understand which of the following mathematical concepts?

a. Commutative property of multiplication
b. Distributive property of multiplication over addition
c. Division as the inverse of multiplication
d. Associative property of multiplication and addition

Answer 1

The student's mistake in simplifying the expression indicates a lack of understanding of the Distributive Property of Multiplication over Addition.

Step-by-step explanation:

When the student simplifies the algebraic expression 2x+3x+5=20 incorrectly to 10x=20, it shows a misunderstanding in the concept of the Distributive Property of Multiplication over Addition. The correct simplification should combine like terms first, giving 5x + 5 = 20, which simplifies further to 5x = 15, and finally dividing by 5 on both sides gives x = 3. The mistake made by the student suggests that they did not distribute the addition correctly across the terms 2x and 3x.