Question

Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10

Given ⇒ 2(x − 4) + 6x = 9x − 10
Step 1 ⇒ 2x − 8 + 6x = 9x − 10
Step 2 ⇒ 2x + 6x − 8 = 9x − 10
Step 3 ⇒ 8x − 8 = 9x − 10
Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Step 5 ⇒ 0 − 8 = x − 10
Step 6 ⇒ −8 = x − 10
Step 7 ⇒ −8 + 10 = x − 10 + 10
Step 8 ⇒ 2 = x + 0
Step 9 ⇒ 2 = x

Which step in solving this equation is justified by the Commutative Property of Addition?
A) Step 1 ⇒ 2x − 8 + 6x = 9x − 10
B) Step 2 ⇒ 2x + 6x − 8 = 9x − 10
C) Step 3 ⇒ 8x − 8 = 9x − 10
D) Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10

Answer 1

Option B i.e. step 2 is the correct answer.

Explanation:

The simplest example of Commutative Property of Addition is as follows:

4 + 2 = 2 + 4

So, in Commutative Property of Addition, we can interchange the position of two or more terms which are in summation operation.

Now, in step 2, we have written

if 2x − 8 + 6x = 9x − 10

then we can write

2x + 6x − 8 = 9x − 10

Therefore, we have interchanged the position of - 8 and 6x in this step 2.

Hence, option B i.e. step 2 is the correct answer.