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.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .