RU-SPB 2020 Problem 91

What is the maximal number of solutions can the equation have $$\max \{a_1x+b_1, a_2x+b_2, \ldots, a_{10}x+b_{10}\}=0$$ where $a_1,b_1, a_2, b_2, \ldots , a_{10},b_{10}$ are real numbers, all $a_i$ not equal to $0$ .