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Help with extraneous solutions??? (algebra 2)?

I'm really confused on these kinds of problems. The directions say Solve each equation. Check for extraneous equations. I'm confused about what an extraneous solution is (I was absent). Can someone please help?

|x-1| = 5x + 10

Thanks in advance! :)

Answers (2)

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solve for (x-1) = 5x + 10 X =-2.75

and -x+1 = 5x + 10 X = -1.5

now put these values back in the original equation

for X =-2.75

LHS 3.75 and RHS -3.75 its is an extraneous solution

for X = -1.5

LHS 2.5 and RHS 2.5 hence its a NON extraneous solution

Reference: an extraneous solution represents a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the original problem