Question

When doing absolute value, do you always have to isolate whatever is in the bars on one side of the equation?

Answer 1

For example, |x+1|-4=-1. Is it absolutely necessary for me to isolate |x+1| on one side of the equal sign to solve the equation?

Answer 2

If you are solving for x, you may have some operations to undo to get to x.
so if you have
|x|=3
and we are solving for x
first recall |x| is sqrt(x^2)

sqrt(x^2)=3
square both sides
x^2=9
not square root both sides

x=pm 3

Answer 3

you don't have to do that first but you are trying to isolate x

Answer 4

so eventually you will have to do it anyways

Answer 5

I don't understand. I tried that equation without isolating the bar part and I only got it right after I isolated that part. In other equations involving absolute value, I usually just remove the bars and work the equation and I get it right. With this one I was only getting one of the right answers.

Answer 6

\[|x+1|=\pm (x+1)\]

Answer 7

you have two equations to solve

Answer 8

\[|x+1|-4=-1\]
\[\pm(x+1)-4=-1\]
\[x+1-4=-1 \text{ or } -(x+1)-4=-1\]

Answer 9

\[x-3=-1 \text{ or } -x-1-4=-1\]
\[x=-1+3 \text{ or } -x-5=-1\]

Answer 10

\[x=2 \text{ or } -x=4\]

Answer 11

\[x=2 \text{ or } x=-4\]

Answer 12

Time for checking!
x=2
|2+1|-4=|3|-4=3-4=-1 GOOD!
x=-4
|-4+1|-4=|-3|-4=3-4=-1 GOOD!

Answer 13

Both of our solutions checked out!

Answer 14

:) thanks a lot