Question

What is the solution set for |x - 6| + 4 = 10

Answer 1

First you have to subtract the 4 from both sides. And then you drop the absolute value sign and solve like a regular equation.

You then have to to it to its negative.

Answer 2

@claritamontano There are two answers for this. x = 12 that I know. What the other value and how do I find it?

Answer 3

So just set it to its negative.


\[\left| x-6 \right| +4=-10\]

Answer 4

that would be your second equation.

Answer 5

Then x would equal -8

I put -8, 12 as my solution set on my test and I got that wrong. That's what I'm trying to figure out...

Answer 6

@claritamontano

Answer 7

okay so what were your choices?

Answer 8

1. {0, 12}
2. {-8, 12} What I put
3. {-12, 0}
4. {-12. -8}

Answer 9

your answer would be 12 not 012.

Answer 10

What do you mean?

Answer 11

I put #2 as my answer, almost everyone in my class put #1 and they got it right.

Answer 12

wait sorry lol answered the wrong question I was looking at my notes and did that problem give me a sec. can I see you steps on how you solved this.?

Answer 13

Do NOT change the RHS to the negative until you have isolated the absolute value. E.g., do NOT use

|x−6|+4=−10

do get the 2nd solution. Isolate the abs value FIRST, then set up both the positive and negative solutions:

|x−6|+4=10
|x−6|=−14

Answer 14

I did it the same way you did it @claritamontano .

x - 6 + 4 = 10
x - 2 = 10
x = 12

x - 6 + 4 = -10
x - 2= -10
x = -8

Answer 15

My teacher taught "drop the bars and negate one equation, then solve"

Answer 16

yeah thats what my teacher said also.

Answer 17

I did just that and got the wrong answer... maybe she graded the test papers wrong :?

Answer 18

Crap, not sure what all that crazyness is.

|x-6|+4=10
|x-6|=6

THEN set up the compound equation:

x-6=6 OR x-6=-6

Answer 19

oh i see thanks debbie i learned something also XD

Answer 20

"drop the bars and negate one equation, then solve" is fine, but only after you isolate the absolute value. Its because of what abs value MEANS.

|x|=6 means that x=6 or x=-6

But |x|+a=6 does NOT mean that |x|+a=6 or |x|+a=-6

Answer 21

I see how you did that Debbie. But I want to know how to get the answer using my teachers method.

Drop the bars.
Negate the equation.
Solve.

Can you show me how you do it, step-by-step please.

Answer 22

Isolate the absolute value expression (get it all by itself on one side of the = sign).
Drop the bars.
Negate the equation.
Solve.

What you are doing is getting the point where you have:

|stuff|=a where a is some number. Once that is true, then you can say that
stuff=a or stuff=-a

WHATEVER the stuff. I always say "put blinders on... don't TOUCH what is inside the abs value sign, just isolate it, then split into 2 equations, one = a and the other = -a".

Answer 23

So you have

|x-6|+4=10
|x-6|=6

THEN set up the compound equation:

x-6=6 OR x-6=-6

Now, can you solve each of those? Those are your 2 solutions.

Answer 24

And dont forget the beauty of algebra - you can ALWAYS CHECK YOUR ANSWER. Notice that your solutions, 12 and -8, do not both work.