###### Example3.5.11

Solve for $$x$$ in the equation $$3(x+2)-8=(5x+4)-2(x+1)\text{.}$$

To solve for $$x\text{,}$$ we will first need to simplify the left side and right side of the equation as much as possible by distributing and combining like terms:

\begin{align*} 3(x+2)-8\amp=(5x+4)-2(x+1)\\ 3x+6-8\amp=5x+4-2x-2\\ 3x-2\amp=3x+2 \end{align*}

From here, we'll want to subtract $$3x$$ from each side:

\begin{align*} 3x-2\subtractright{3x}\amp=3x+2\subtractright{3x}\\ -2\amp=2 \end{align*}

As the equation $$-2=2$$ is not true for any value of $$x\text{,}$$ there is no solution to this equation. We write the solution set as: $$\emptyset\text{.}$$

in-context