[tex]a) \frac{5 - x}{2} - \frac{1 - 3x}{5} = 4 \: | \times 10[/tex]
[tex]5(5 - x) - 2(1 - 3x) = 40[/tex]
[tex]25 - 5x - 2 + 6x = 40[/tex]
[tex] - 5x + 6x = 40 - 25 + 2[/tex]
[tex]x = 17 \: \in \: \mathbb{R}[/tex]
[tex]b) \frac{x - 1}{2} - \frac{2x - 1}{4} + 2 = x + 3 \: | \times 4[/tex]
[tex]2(x - 1) - 2x + 1 + 8 = 4x + 12[/tex]
[tex]2x - 2 - 2x + 1 + 8 = 4x + 12[/tex]
[tex]2x - 2x - 4x = 12 + 2 - 1 - 8[/tex]
[tex] - 4x = 5 \: | \times ( - 1)[/tex]
[tex]4x = - 5[/tex]
[tex]x = - \frac{5}{4} \: \in \: \mathbb{R}[/tex]
[tex]c)2(x - 1) - 3(x + 2) = 5[/tex]
[tex]2x - 2 - 3x - 6 = 5[/tex]
[tex]2x - 3x = 5 + 2 + 6[/tex]
[tex] - x = 13 \: | \times ( - 1)[/tex]
[tex]x = - 13 \: \in \: \mathbb{R}[/tex]
[tex]d)3(x + 1) - 4(x - 2) = 6[/tex]
[tex]3x + 3 - 4x + 8 = 6[/tex]
[tex]3x - 4x = 6 - 3 - 8[/tex]
[tex] - x = - 5 \: | \times ( - 1)[/tex]
[tex]x = 5 \: \in \: \mathbb{R}[/tex]
[tex]e)3(x - 2) - ( - 6 + x) \times ( - 2) = - 18[/tex]
[tex]3x - 6 - (12- 2x) = - 18[/tex]
[tex]3x - 6 -12+ 2x = - 18[/tex]
[tex]3x + 2x = - 18+6+12 [/tex]
[tex]5x = 0[/tex]
[tex]x = 0\: \in \: \mathbb{R}[/tex]
[tex]f) {(x - 1)}^{2} - (x + 2)( x - 1) + 1 = 0[/tex]
[tex] {x}^{2} - 2x + 1 - ( {x}^{2} - x + 2x - 2) + 1 = 0[/tex]
[tex] {x}^{2} - 2x + 1 - ( {x}^{2} + x - 2) + 1 = 0[/tex]
[tex] {x}^{2} - 2x + 1 - {x}^{2} - x + 2 + 1 = 0[/tex]
[tex] {x}^{2} - {x}^{2} - 2x - x = - 1 - 2 - 1[/tex]
[tex] - 3x = - 4 \: | \times ( - 1)[/tex]
[tex]3x = 4[/tex]
[tex]x = \frac{4}{3} \: \in \: \mathbb{R}[/tex]
