Solve the equation $|x-7|-3|2x+1|=0$ This equation is very unfamiliar with me, I never seen things like that because I always solved equations of the form $|\text{something}|=\text{things}$ but never seen equations that look like $|\text{something}|=|\text{things}|$. So if I learn how to solve it I will be able to solve questions that looks like it. Thank you;

One way to handle this kind of equation is to notice that any solution to that equation is a solution to one of
$$
\frac{x-7}{2x+1}=\pm3
$$
then solve each equation and toss answers that don't fit.
$$
\frac{x-7}{2x+1}=3\implies x=-2
$$
and
$$
\frac{x-7}{2x+1}=-3\implies x=\frac47
$$
Both of these fit the original equation and are therefore all of the solutions.
Note that if $2x+1=0$ we have $x-7=-\frac{15}{2}$ so the equation is not satisfied if the denominator is $0$.
