Question

Below are the steps to solve an equation:

Step 1: |x - 5| + 2 = 5
Step 2: |x - 5| = 5 - 2
Step 3: |x - 5| = 3

Which of the following is a correct next step to solve the equation?

x + 5 = -3

-x - 5 = 3

x - 5 = -3

x + 5 = 3

Answer 1

I think it's A.

Answer 2

mm.... I would argue that none of those REALLY give the correct next step, because the next step is to set up a COMPOUND equation that does not involve abs value.

But it is definitely not A, because A is not either of the equations needed in the compound equation.

Answer 3

C.

Answer 4

After step 3, you eliminate the absolute value. that leaves you with x-5=3 or x-5=-3

Answer 5

The thing to keep in mind about about absolute value expressions is that abs value is simply the DISTANCE from 0.

So |{something}|=3 means that the {something} (whatever is INSIDE the abs value expression) is 3 units from 0.

Now, how does something get to be 3 units from 0?? It's either 3 units to the RIGHT of 0, or 3 units to the LEFT of 0, right?

So if it's 3 units to the right, then that means that: {something}=3
And if it's 3 units to the left, then that means that: {something}=-3

So there are TWO POSSIBILITIES:... and you get a COMPOUND equation. Not a SINGLE equation.

Answer 6

Right, I got you . . .

Answer 7

Can you tell me what those lines mean again? Say |-9| it becomes positive 9 right?

Answer 8

The problem with your choice A though, is that it isn't EITHER of the equations in the compound equation. See, in A, they changed the {something}, from (x-5) to (x+5). But the {something} doesn't change when you set up the compound equation

Answer 9

@greenlegodude57 I just told you it's C and why it's C ._.

Answer 10

Well I want to see @DebbieG 's opinion.

Answer 11

|a| means the "absolute value of a", which means the DISTANCE that a is from 0.

So: |5| = 5 since 5 is 5 units from 0.

and |-5|=5 since -5 is 5 units from 0.

So yes, you can think of it as "taking the absolute value makes it positive" - but always remember WHY: it's because it means "distance from 0".

Answer 12

Ohhh, I got it I never really understood that until now. Thanks a lot.

Answer 13

But what would it mean in an equation?

Answer 14

Like I said, the solution really REQUIRES a compound equation. But I guess that since it is worded: "which is a correct next step" then C is an adequate answer, because it's the ONLY one that is PART of the solution to the equation.

Answer 15

Ohhh, but I don't get why you change positive 3 to negative 3.

Answer 16

As above: once you get the absolute value expression "isolated" (which they did for you) you have:

|x - 5| = 3

So what does that mean? It means that the {something} inside the abs value, is 3 units from 0. So, that {something}is either =3, or =-3. So to rewrite the equivalent COMPOUND equation without abs value, you have:

x - 5 = 3 OR x - 5 = -3

ONE of those has to be true, since |x - 5| = 3, right? That's exactly what |x - 5| = 3 MEANS, after all. :)

Answer 17

Ohhh so x - 5 = 3 and x - 5 = -3 are the same thing?

Answer 18

Well, you need BOTH. Becauset here are two possibilities:

One is that: x - 5 = 3
The other is that: x - 5 = -3

In EITHER case, you have |x - 5| = 3.

That's why I'm not crazy about how this question is worded... lol. If you are just learning about solving abs value equations, it's important to understand that you have to break it into the TWO possibiliites, and solve each of those separately.

Answer 19

Oh right, I learned that. So your gonna have 2 answers or sometimes infinite answers and sometimes no answers.

Answer 20

No no no... not the "same thing", but the "two possibilities". BOTH will give a solution to the equation |x - 5| = 3

If x - 5 = 3 then you get: x=8 right? (just solve the equation.
If x - 5 = -3 then you get x=2 right?

So BOTH x=8 and x=2 are solutions to the ORIGINAL, ABSOLUTE VALUE equation:
|x - 5| = 3

Just try them both in the original equation, you'll see that they both work.

Answer 21

Right, so they're not the same thing but they're both solutions, okay thanks a lot.

Answer 22

you're welcome. :)

Answer 23

its totaly d