Solution - Absolute value equations

Use the rules:
$$\left|x\right|=\left|y\right|$$ → $$x=\pm y$$ and $$\left|x\right|=\left|y\right|$$ → $$\pm x=y$$
to write all four options of the equation
$$\left|x\right|=|x-\frac{7}{3}|$$
without the absolute value bars:

When simplified, equations $$x=+y$$ and $$+x=y$$ are the same and equations $$x=-y$$ and $$-x=y$$ are the same, so we end up with only 2 equations:

The equation is false so it has no solution.

Each line represents the function of one side of the equation:
$$y=\left|x\right|$$
$$y=|x-\frac{7}{3}|$$
The equation is true where the two lines cross.