[tex]a)5 |x + 3| = 6 - 7 |x + 3| [/tex]
[tex]5 |x + 3| + 7 |x + 3| = 6[/tex]
[tex] |x + 3| (5 + 7) = 6[/tex]
[tex]12 |x + 3| = 6 \: | \div 6[/tex]
[tex]2 |x + 3| = 1[/tex]
[tex] |x + 3| = \frac{1}{2} [/tex]
[tex]1)x + 3 = \frac{1}{2} [/tex]
[tex]x = \frac{1}{2} - 3[/tex]
[tex]x = \frac{1}{2} - \frac{6}{2} [/tex]
[tex]x = - \frac{5}{2} [/tex]
[tex]2)x + 3 = - \frac{1}{2} [/tex]
[tex]x = - \frac{1}{2} - 3[/tex]
[tex]x = - \frac{1}{2} - \frac{6}{2} [/tex]
[tex]x = - \frac{7}{2} [/tex]
[tex]b) |x + 1| = |2x - 2| [/tex]
[tex]1)x + 1 = 2x - 2[/tex]
[tex]x - 2x = - 2 - 1[/tex]
[tex] - x = - 3 \: | \times ( - 1)[/tex]
[tex]x = 3[/tex]
[tex]2) - (x + 1) = 2x - 2[/tex]
[tex] - x - 1 = 2x - 2[/tex]
[tex] - x - 2x = - 2 + 1[/tex]
[tex] - 3x = - 1 \: | \times ( - 1)[/tex]
[tex]3x = 1 [/tex]
[tex]x = \frac{1}{3} [/tex]
[tex]3)x + 1 = - (2x - 2)[/tex]
[tex]x + 1 = - 2x + 2[/tex]
[tex]x + 2x = 2 - 1[/tex]
[tex]3x = 1[/tex]
[tex]x = \frac{1}{3} [/tex]
[tex]4) - (x + 1) = - (2x - 2)[/tex]
[tex] - x - 1 = - 2x + 2[/tex]
[tex] - x + 2x = 2 + 1[/tex]
[tex]x = 3[/tex]
