[tex] |x - 1| + |2x - 2| + |3x - 3| + ... + |9x - 9| = 90[/tex]
[tex] |x - 1| + |2(x - 1)| + |3(x - 1)| + ... + |9(x - 1)| = 90[/tex]
[tex] |x - 1| + |2| \times |x - 1| + |3| \times |x - 1| + ... + |9| \times |x - 1| = 90[/tex]
[tex] |x - 1| + 2 |x - 1| + 3 |x - 1| + ... + 9 |x - 1| = 90[/tex]
[tex] |x - 1| (1 + 2 + 3 + ... + 9) = 90[/tex]
[tex] |x - 1| \times \frac{9(9 + 1)}{2} = 90[/tex]
[tex] |x - 1| \times \frac{9 \times 10}{2} = 90[/tex]
[tex] |x - 1| \times 9 \times 5 = 90[/tex]
[tex]45 |x - 1| = 90 \: | \div 45[/tex]
[tex] |x - 1| = 2[/tex]
[tex]1)x - 1 = - 2[/tex]
[tex]x = - 2 + 1[/tex]
[tex]x = - 1[/tex]
[tex]2)x - 1 = 2[/tex]
[tex]x = 2 + 1[/tex]
[tex]x = 3[/tex]
