Równania i nierówności liniowe. Rozwiąż równania i nierówności w załącznikach.

a) [latex]2-frac{1+x}{4}=frac{x-1}{3} / cdot 12\ 24-3(1+x)=4(x-1)\ 24-3-3x=4x-4\ -3x-4x=-4-21\ -7x=-25\ x=frac{25}{7}\ x=3frac{4}{7}[/latex] b) [latex]7+frac{1+x}{5}=frac{2x-7}{3} / cdot 15\ 105-3(1+x)=5(2x-7)\ 105-3-3x=10x-35\ -3x-10x=-35-102\ -7x=-67\ x=frac{67}{7}\ x=9frac{3}{7}[/latex] c) [latex]frac{x}{5}-1frac23=frac{2x}{3}+2frac{1}{2}\ frac{x}{5}-frac{2x}{3}=2frac{1}{2}+1frac23\ frac{3x}{15}-frac{10x}{15}=frac{5}{2}+frac{5}{3}\ -frac{7x}{15}=frac{15}{6}+frac{10}{6}\ -frac{7}{15}x=frac{25}{6} / cdot(-frac{15}{7})\ x=frac{25}{6}(-frac{15}{7})\ x=-frac{375}{42}\ x=-8frac{39}{42}\ x=-8frac{13}{14}[/latex] d) [latex]frac{x}{2}-2frac23=frac{2x}{5}-1frac{1}{2}\ frac{x}{2}-frac{2x}{5}=-1frac{1}{2}+2frac23\ frac{5x}{10}-frac{4x}{10}=-frac{5}{2}+frac{7}{3}\ frac{x}{10}=-frac{15}{6}+frac{14}{6}\ frac{1}{10}x=-frac{1}{6} / cdot(-frac{10}{1})\ x=frac{10}{6}\ x=1frac{4}{6}\ x=1frac{2}{3}[/latex] e) [latex]frac{x}{4}+3frac{2}{3}=frac{2x}{3}-4frac{3}{8}\ frac{x}{4}-frac{2x}{3}=-frac{35}{8}-frac{11}{3}\ frac{3x}{12}-frac{8x}{12}=-frac{105}{24}-frac{88}{24}\ -frac{5x}{12}=-frac{193}{24}\ x=frac{193}{24}frac{12}{5}\ x=frac{193}{60}\ x=3frac{13}{60}[/latex] f) [latex]2x-11leq3(5x-2)\ 2x-11leq15x-6\ 2x-15xleq-6+11\ -13xleq5\ xgeq-frac{5}{13}\ \ x epsilon <-frac{5}{13};+infty)[/latex] g) [latex]2(x-11)leq3x-2\ 2x-22leq3x-2\ 2x-3xleq-2+22\ -xleq-20\ xgeq20\ \ x epsilon <20;+infty)[/latex] h) [latex]2-3(x-11)leq3(5x+1)\ 2-3x+11leq15x+3\ -3x+13leq15x+3\ -3x-15xleq3-13\ -18xleq-10\ xgeqfrac{10}{18}\ xgeqfrac{5}{9} \ x epsilon