Answer:
[tex]\large\boxed{x=\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right\\\\|x-4|=\left\{\begin{array}{ccc}x-4&for&x-4\geq0\to x\geq4\\-(x-4)&for&x<4\end{array}\right[/tex]
[tex](1)\ x<4\\\\-(x-4)-5=3(x-1)\qquad\text{use the distributivep property}\\\\-x-(-4)-5=3x+(3)(-1)\\\\-x+4-5=3x-3\qquad\text{combine like terms}\\\\-x+(4-5)=3x-3\\\\-x-1=3x-3\qquad\text{add 1 to both sides}\\\\-x-1+1=3x-3+1\\\\-x=3x-2\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-2\\\\-4x=-2\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{-2}{-4}\\\\x=\dfrac{1}{2}\in(1)[/tex]
[tex](2)\ x\geq4\\\\x-4-5=3(x-1)\\\\x+(-4-5)=3x-3\\\\x-9=3x-3\qquad\text{add 9 to both sides}\\\\x-9+9=3x-3+9\\\\x=3x+6\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\x-3x=3x-3x+6\\\\-2x=6\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{6}{-2}\\\\x=-3\notin(2)[/tex]
