Answer:
[tex]x=-\frac{3}{4} \\x=-\frac{1}{6}[/tex]
Step-by-step explanation:
Examine the two possible cases associated with the expression inside the absolute value symbol:
Case 1) x-1 is larger or equal zero, and in such case its absolute value is directly x-1.
Then we solve for x in the equation:
[tex]x-1=5x+2\\-1-2=5x-x\\-3=4x\\x=-\frac{3}{4}[/tex]
Case 2) x-1 is less than zero, in which case its absolute value is the opposite of the expression: -x+1
Next we solve for x in the equation:
[tex]-x+1=5x+2\\1-2=5x+1\\-1=6x\\x=-\frac{1}{6}[/tex]
Therefore there are two possible solutions: [tex]x=-\frac{3}{4} \\x=-\frac{1}{6}[/tex]
