Question

Where do you break up the problem to have to solutions?
Solve for x: 2|x - 3| + 1 = 7

Answer 1

After you get the absolute value by itself...

Subtract 1 from both sides
Divide both sides by 2

THEN you make it 2 equations

Answer 2

How do you get it by itself, like the solution inside the bars?

Answer 3

Alright so we have

\[\large 2|x - 3| + 1 = 7\]
Subtract 1 from both sides
\[\large 2|x - 3| = 6\]
Divide both sides by 2
\[\large |x - 3| = 3\]
Now you break it up into 2 equations...
\[\large x - 3 = 3\]
and
\[\large x - 3 = -3\]

Answer 4

Okay that confused me a bit? How do you know when to separate the equation?

Answer 5

So you see how I went through the steps? When I got to the step where the ONLY thing left on one side of the equation is the absolute value?

|x - 3| = 3
^
This is the only thing on this side of the equation...

When that is the case...that is when you break it up

Answer 6

oh okay, that makes sense now !!!! lol & would that be the answer or do i keep going?

Answer 7

Well That IS where you separate the equation...

Do you need to solve for 'x' ?

Answer 8

yes i need to solve for X. I got 0 on one of the solutions

Answer 9

0 is one of the solutions

\[\large x - 3 = -3\]

But what about

\[\large x - 3= 3\]

Answer 10

it would be 0 again:?

Answer 11

\[\large 0 - 3 \ne 3\]

Answer 12

6?

Answer 13

There we go!

So your answers are both 0 and 6

Answer 14

Thank You!!

Answer 15

No problem!