Five books of five different colors are placed on a shelf. the goldgold book is placed between the orangeorange and pinkpink books, and these three books are consecutive. the graygray book is not leftmost on the shelf and the pinkpink book is not rightmost on the shelf. the brownbrown book is separated from the pinkpink book by two books. if the graygray book is not next to the brownbrown book, what is the complete ordering of the books?

We have to complete the order of five different colored books.

Step 1: Gold book is placed between orange and pink book and they are placed consecutive. So, we get

Orange book , Gold book, Pink book

Step 2: Gray book is not leftmost on the shelf and the pink book is not rightmost on the shelf. Still we get,

Orange book , Gold book, Pink book

Step 3: The brown book is separated from the pink book by two books.

So we get,

Brown book, Orange book , Gold book, Pink book

We did not take brown book separated from the right side of pink book, otherwise we would get total six books, which is not possible, As we have to order total five books.

Step 4: The gray book is not next to the brown ​book. So, we get as:

Brown book, Orange book , Gold book, Pink book , Gray book

Here, we can also observe that the gray book is not leftmost on the shelf and the pink book is not rightmost on the shelf.

So, the correct order of these five books are:

Brown book , Orange book, Gold book, Pink book, Gray book.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.