11.36 Solve graphically the equation

$$
|x-1|+2x-5=0
$$
11.36 Let's write the equation as $|x-1|=5-2 x$. Since $|x-1| \geq 0$ for any $x$,

![](https://cdn.mathpix.com/cropped/2024_05_21_1e3d8d2f6605ac23e2a5g-359.jpg?height=342&width=466&top_left_y=273&top_left_x=690)

Fig. 11.11

and $\quad 5-2 x \geq 0$, i.e., $x \leq 2.5$.

Consider the functions $y_{1}=|x-1|, y_{2}=5-2 x$ and plot their graphs on the same diagram for $\quad x \leq 2.5 \quad$ (Fig.

11.12). The solution to the given equation is the points of intersection of these graphs. Using Fig. 11.12, we establish that $x=2$.

Answer: $x=2$.