Verified answer

[tex]5 \cdot|0.5x + 1| - 7 = - 4.5 \\ 5\cdot |0.5x + 1| = - 4.5 + 7 \\ 5\cdot |0.5x + 1| = 2.5 \\ |0.5x + 1| = \frac{2.5}{5} \\ |0.5x + 1| = 0.5 \\ 0.5x + 1 = 0.5~~~~~~~~~~~~~0.5x + 1 = - 0.5 \\ 0.5x = 0.5 - 1 ~~~~~~~~~~~~~0.5x = - 0.5 - 1 \\ 0.5x = - 0.5~~~~~~~~~~~~~~~~~~~~~~0.5x = - 1.5 \\ x_1 = - 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~x_2 = - 3 \\ \boxed{otvet:x_1= -1~~;~~x_2= -3}[/tex]