1. ## No Solution

I have been working this problem out and the answer in the book is stating no solution. I am getting x=-4.

2(x+3)-5=5x-3(1+x)

2. $\displaystyle \displaystyle 2(x+3) - 5 = 5x - 3(1 + x)$

$\displaystyle \displaystyle 2x + 6 - 5 = 5x - 3 - 3x$

$\displaystyle \displaystyle 2x + 1 = 2x - 3$.

They are correct, there is not a solution - the two lines are parallel and therefore never meet...

I have been working this problem out and the answer in the book is stating no solution. I am getting x=-4.

2(x+3)-5=5x-3(1+x)
If x= -4, 2(-4+ 3)- 5= 2(-1)+ 5= -2+ 5= 3 but 5(-4)- 3(1+(-4))= -20- 3(-3)= -20+ 9= -11. They are not at all the same!

Perhaps if you showed us how you got -4, we could point out a mistake.

I have been working this problem out and the answer in the book is stating no solution. I am getting x=-4.

2(x+3)-5=5x-3(1+x)
$\displaystyle 2x+6-5=5x-3-3x\;\;?$

$\displaystyle 2x+1=2x-3\;\;$

In algebraic terms, the question is

"For what x is $\displaystyle 2x+1=2x-3\;\;?$"

The answer is "no x", since $\displaystyle 2x-2x+1\ne\ 2x-2x-3$

$\displaystyle 1\ne\ -3$