ex 5
[tex]\displaystyle\\\rm\\\frac{2x-1}{3}+3x-4=\frac{1-2x}{4}-\frac{5}{12} \\ \\ \\\frac{4 \cdot (2x-1)}{12} + \frac{12 \cdot (3x-4)}{12} = \frac{3\cdot(1-2x)}{12}-\frac{5}{12} \\ \\ \\\frac{8x-4}{12} + \frac{36x-48}{12} = \frac{3-6x}{12}-\frac{5}{12} \\ \\ \\8x - 4 + 36x - 48 = 3 - 6x - 5 \\ \\44x - 52 = -6x -2 \\ \\50x - 52 = -2\\ \\50x = -2 + 52 \\ \\50x = 50 \\ \\\boxed{x=1}[/tex]
[tex]\displaystyle\\\rm\\2 + mx - 3x = x \cdot (3m - 2) + 4 \\ \\2 + m - 3 = 3m -2 + 4 \\ \\m - 1 = 3m + 2 \\ \\2m + 2 = -1 \\ \\2m = -1 - 2 \\ \\2m = -3 \\ \\\boxed{m=\frac{-3}{2}}[/tex]
ex 6
[tex]\displaystyle\\\rm\\|\frac{3x+1}{2} |=10 \implies I) \ \frac{3x+1}{2}=10 \ SAU \ II) \ \frac{3x+1}{2}=-10 \\ \\ \\I) \ \frac{3x+1}{2} = 10 \rightarrow 3x + 1 = 20 \rightarrow 3x = 19 \rightarrow \boxed{x=\frac{19}{3}} \\ \\ \\II) \ \frac{3x+1}{2} = -10 \rightarrow 3x + 1 = -20 \rightarrow 3x = -21 \rightarrow \boxed{x=-7} \\ \\ \\\\\x \in \{-7, \frac{19}{3}\}[/tex]
