Question

Which of the following are solutions to |x-1|=5x+2

Answer 1

`x=-(3)/(4) \\x=-(1)/(6)`

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:

`x-1=5x+2\\-1-2=5x-x\\-3=4x\\x=-(3)/(4)`

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:

`-x+1=5x+2\\1-2=5x+1\\-1=6x\\x=-(1)/(6)`

Therefore there are two possible solutions:
`x=-(3)/(4) \\x=-(1)/(6)`