# Linear Application Question (basic)

• Jun 24th 2012, 11:15 AM
allyourbass2212
Linear Application Question (basic)
Part of the expression in a book reads:
$\displaystyle x+(x + 1) = 25$
which becomes
$\displaystyle 2x + 1 = 25$

My question is how does the above expression become $\displaystyle 2x+1=25$?

I thought when you see an expression such as $\displaystyle x+(x+1)$ there is a hidden integer, a 1 therefore it should read $\displaystyle x+1(x+1)=25$. If that is the case shouldn't it be $\displaystyle 2x + 2 = 25$?

Obviously I am not understanding it correctly, I just wanted to show my incorrect logic.

Thanks
• Jun 24th 2012, 11:44 AM
Reckoner
Re: Linear Application Question (basic)
Quote:

Originally Posted by allyourbass2212
My question is how does the above expression become $\displaystyle 2x+1=25$?

$\displaystyle x+(x+1) = 25$

$\displaystyle \Rightarrow (x+x) + 1 = 25$ (Associativity of addition)

$\displaystyle \Rightarrow x(1+1) + 1 = 25$ (Distributive property)

$\displaystyle \Rightarrow x\cdot2 + 1 = 25$ (1+1=2)

$\displaystyle \Rightarrow 2x + 1 = 25$ (Commutativity of multiplication)

Normally we wouldn't show all of those steps. In general, to add like terms (terms with the same variables and powers), you add their coefficients. So, for example,

$\displaystyle 2x + x = 3x$

$\displaystyle a + a + b = 2a + b$

$\displaystyle 4xy^2 + 3xy^2 = 7xy^2$

Quote:

Originally Posted by allyourbass2212
I thought when you see an expression such as $\displaystyle x+(x+1)$ there is a hidden integer, a 1 therefore it should read $\displaystyle x+1(x+1)=25$. If that is the case shouldn't it be $\displaystyle 2x + 2 = 25$?

Okay, but this "hidden integer" is being multiplied, not added.