Are "5" and "4x" algebraic expressions?
In an elementary textbook I have, an algebraic expression is defined as
The expressions in which the numbers, or variables, or both, are connected by operational signs (+, - etc.) are called algebraic expressions.
For example $5$, $4x$, $a+b$, $x-y$ etc.
The question is that how is $5$ or $4x$ an algebraic expression when it does not have any operational sign?
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$\begingroup$$5=5+0$, $4x=4x+0$. In reality, they have an operational sign.
Or $5=5+7-7$ or $4x=4x+6-6$.
Good question. It's due to what I like to call "the invisible plus sign."
We're really talking about $+5$ and $+4x$.
You need to aware of the invisible plus sign when you manipulate an expression algebraically.
For example, solve for $x$:
$$5+4x=0$$
The first step is to move the $+5$ to the right hand side of the equation. When you do so, it changes signs.
$$4x=0-5=-5$$
(The fact that it's sign becomes opposite means that it has a sign.)
Note that when those terms are part of a larger expression, only the initial term has an "invisible" plus sign. The "$+$" on front of $4x$ is quite apparent.
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