Question

|x - 1| = 5x + 10
I know the answers are x = -11/4 or x = -3/2 but how do i find out if one is extraneous or not?

Answer 1

try each solution in the original equation and see if it works

for example, with x= -11/4
|-11/4 - 1| =? 5* -11/4 +10
|-11/4 - 4/4| = ? -11/4 +40/4
|-15/4| = ? 29/4
15/4 = ? 29/4

Answer 2

Ok thanks. Real quick, what happens to the 5 in step 2?

Answer 3

I lost it!
(-55+40)/4 = -15/4

but on the left side of the = you have
| -15/4|= + 15/4
so it does not work

Answer 4

in other words x= -11/4 ends up with
+15/4 = ? - 15/4 which is not true

on the other hand
|-3/2 - 1 | = ? 5(-3/2) +10
5/2 = ? -15/2 + 20/2
5/2 = ? 5/2
which is true

Answer 5

Oh ok thank you!

Answer 6

yw