Rozwiąż nierówność |2x-7|-|3x+5|>=0 Rozwiąż równanie: |4x-8|+|(x-2)/3|=8

1) [latex]|2x-7|-|3x+5| geq 0 \ \ dla x in (-infty; -frac{5}{3} angle \ -2x+7-(-3x-5) geq 0 \ -2x+7+3x+5 geq 0 \ x+12 geq 0 \ x geq -12 \ x in langle -12; -frac{5}{3} angle \ \ dla x in langle -frac{5}{3}; frac{7}{2} angle \ -2x+7-(3x+5) geq 0 \ -2x+7-3x-5 geq 0 \ -5x+2 geq 0 \ -5x geq -2 \ x leq frac{2}{5} \ x in langle -frac{5}{3}; frac{2}{5} angle[/latex] [latex]\ dla x in langle frac{7}{2}; infty) \ 2x-7-(3x+5) geq 0 \ 2x-7-3x-5 geq 0 \ -x-12 geq 0 \ -x geq 12 \ x leq -12 \ x in emptyset[/latex] Odp.: [latex]x in langle -12; frac{2}{5} angle[/latex] 2) [latex]|4x-8|+|frac{x-2}{3}|=8 \ \ dla x in (-infty;2 angle \ -4x+8 - frac{x-2}{3} = 8 \ -12x+24-x+2=24 \ -13x+2=0 \ -13x=-2 \ x=frac{2}{13} in (-infty;2 angle \ \ dla x in langle 2; infty) \ 4x-8+frac{x-2}{3}=8 \ 12x-24+x-2=24 \ 13x-26=24 \ 13x=50 \ x=frac{50}{13} in langle 2; infty)[/latex] Odp.: [latex]x in { frac{2}{13}, frac{50}{13} }[/latex]