Introductory Algebra for College Students (7th Edition)

$9+3(x-2)$, simplifies to $\quad 3x+3$
"nine increased by"$\quad\rightarrow 9+...$ " the product of $3$ and ..."$\quad\rightarrow 3\cdot(...)$ "2 less than a number"$\quad\rightarrow (x-2)$ the expression translates to$:\qquad 9+3(x-2)$ Using the distributive property, $9+3(x-2)=9+3x-3\cdot 2$ $=9+3x-6$ ... group like terms ($9$ and $3x$ can change places) $=3x+(9-6)$ = $3x+3$