\frac{2}{3}}} \right. \; \left [ {{4x=-2,\; x \leq \frac{2}{3}} \atop {2x=6,\; x>\frac{2}{3}}} \right. " alt="|2-3x|=x+4\; \; \to \; \; \left [ {{2-3x=x+4,\; x \leq \frac{2}{3}} \atop {2-3x=-(x+4),\; x>\frac{2}{3}}} \right. \; \left [ {{4x=-2,\; x \leq \frac{2}{3}} \atop {2x=6,\; x>\frac{2}{3}}} \right. " align="absmiddle" class="latex-formula">
\frac{2}{3}}} \right. \left [ {{x=-\frac{1}{2}} \atop {x=3}} \right. \\\\b)\; \; 5-|2-3x|=x-1\\\\|2-3x|=6-x\; \; \to \; \; \left [ {{2-3x=6-x,\; x \leq \frac{2}{3}} \atop {2-3x=-(6-x),\; x>\frac{2}{3}}} \right. \; \left [ {{2x=-4} \atop {4x=8}} \right. \; \left \{ {{x=-2} \atop {x=2}} \right. " alt="\left [ {{4x=-2,\; x \leq } \atop {2x=6,\; x>\frac{2}{3}}} \right. \left [ {{x=-\frac{1}{2}} \atop {x=3}} \right. \\\\b)\; \; 5-|2-3x|=x-1\\\\|2-3x|=6-x\; \; \to \; \; \left [ {{2-3x=6-x,\; x \leq \frac{2}{3}} \atop {2-3x=-(6-x),\; x>\frac{2}{3}}} \right. \; \left [ {{2x=-4} \atop {4x=8}} \right. \; \left \{ {{x=-2} \atop {x=2}} \right. " align="absmiddle" class="latex-formula">
\frac{2}{3}}} \right. \; \left [ {{2x=-4} \atop {4x=8}} \right. \; \left \{ {{x=-2} \atop {x=2}} \right. \\\\Proverka:\; 1)\; x=-\frac{1}{2}:\; |5-|2+3\cdot \frac{1}{2}|\, |=|5-\frac{7}{2}|=\frac{3}{2}\; ;\\\\x-1=-\frac{1}{2}-1=-\frac{1}{2}-1=-\frac{3}{2}\; ;\\\\\frac{3}{2}\ne -\frac{3}{2}\\\\2)\; \; x=3:\; \; |5-|2-3\cdot 3||=|5-7|=|-2|=2\; ;\\\\x-1=3-1=2\; ;\\\\2=2" alt="b)\; \; 5-|2-3x|=x-1\\\\|2-3x|=6-x\; \; \to \; \; \left [ {{2-3x=6-x,\; x \leq \frac{2}{3}} \atop {2-3x=-(6-x),\; x>\frac{2}{3}}} \right. \; \left [ {{2x=-4} \atop {4x=8}} \right. \; \left \{ {{x=-2} \atop {x=2}} \right. \\\\Proverka:\; 1)\; x=-\frac{1}{2}:\; |5-|2+3\cdot \frac{1}{2}|\, |=|5-\frac{7}{2}|=\frac{3}{2}\; ;\\\\x-1=-\frac{1}{2}-1=-\frac{1}{2}-1=-\frac{3}{2}\; ;\\\\\frac{3}{2}\ne -\frac{3}{2}\\\\2)\; \; x=3:\; \; |5-|2-3\cdot 3||=|5-7|=|-2|=2\; ;\\\\x-1=3-1=2\; ;\\\\2=2" align="absmiddle" class="latex-formula">
