Absolute Value Equations

A remote-controlled car's distance from a starting point (in meters) is given by $|2t-3|$ meters after $t$ seconds. At what time(s) is the car exactly $t+1$ meters from the start? Solve for $t$.

Find all real numbers $x$ that satisfy the equation $|2x - 1| = 3x - 6$.

A robot's distance from its starting point is $|x-2|$ meters, and its distance from a beacon is $2x-1$ meters, where $x$ is the time in minutes. Find all times $x$ when the two distances are equal.