To actively practice solving absolute value equations requiring prior isolation, solve the given equations $|3x - 5| - 1 = 6$ and $|4x - 3| - 5 = 2$. For the first equation, isolate the absolute value by adding $1$ to both sides, which results in $|3x - 5| = 7$. Generating the equivalent equations yields $3x - 5 = -7$ or $3x - 5 = 7$. Adding $5$ and dividing by $3$ for each case provides the solutions $x = -\frac{2}{3}$ or $x = 4$. For the second equation, adding $5$ to both sides isolates the absolute value, producing $|4x - 3| = 7$. The equivalent equations are $4x - 3 = -7$ or $4x - 3 = 7$. Adding $3$ and dividing by $4$ evaluates to the final solutions $x = -1$ or $x = \frac{5}{2}$.