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

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

Step-by-step 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.

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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