\begin{aligned}
3x – 7 &= 11 && \text{Start with the equation.} \\[6pt]
3x &= 18 && \text{Add 7 to both sides.} \\[6pt]
x &= 6 && \text{Divide both sides by 3.}
\end{aligned}

The solution is [latex]x = 6[/latex].

Solve [latex]4x - 5 = 2x + 7[/latex].

\begin{aligned}
4x – 5 &= 2x + 7 && \text{Start with the equation.} \\[6pt]
4x – 2x – 5 &= 7 && \text{Subtract $2x$ from both sides.} \\[6pt]
2x – 5 &= 7 && \text{Simplify.} \\[6pt]
2x &= 12 && \text{Add 5 to both sides.} \\[6pt]
x &= 6 && \text{Divide both sides by 2.}
\end{aligned}

The solution is [latex]x = 6[/latex].

\begin{aligned}
x^2 – 5x + 6 &= 0 && \text{Start with the quadratic} \\[6pt]
(x – 2)(x – 3) &= 0 && \text{Factor the trinomial} \\[6pt]
x – 2 &= 0 \quad \text{or} \quad x – 3 = 0 \\[6pt]
x &= 2 \quad \text{or} \quad x = 3
\end{aligned}

The solutions are [latex]x = 2[/latex] and [latex]x = 3[/latex].