Question: Why $5x$ and $3x$
1. The problem asks why we use $5x$ and $3x$ in algebraic expressions.
2. In algebra, $x$ represents a variable, and the numbers in front of $x$ are coefficients.
3. $5x$ means $5$ times the variable $x$, and $3x$ means $3$ times the variable $x$.
4. Coefficients tell us how many times to count the variable.
5. For example, if $x=2$, then $5x=5\times 2=10$ and $3x=3\times 2=6$.
6. Using coefficients helps us write expressions compactly and perform operations like addition and subtraction easily.
7. When adding $5x$ and $3x$, we combine coefficients: $5x+3x=(5+3)x=8x$.
8. This is because $x$ is common in both terms, so we add the numbers in front.
9. Understanding coefficients is fundamental to working with algebraic expressions.