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

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.