Question

Which statement has the solution shown on the number line?



|x – 2| = 1

|2x – 2| = 6

|3x – 3| = 6

none of the above



ON THE NUMBER LINE, THE NUMBERS -1 and 3 are both marked.

Answer 1

Let's take these each in turn.

|x-2| = 1
gives all the numbers that are a distance of 1 unit from 2. Agreed? What are those two numbers?

Answer 2

wait what am i supposed to do?

Answer 3

I'm helping you understand what are the solutions for each of these equations so you can compare them with the given solutions of -1 and 3.

If we find an equation which has solutions -1 and 3, then that equation is the answer to your problem.

Answer 4

So the first question is: what are the solutions to
|x-2| = 1
?

Answer 5

do i plug in -1 and -3 in there or what?

Answer 6

No, let's not go down that road.

Geometrically
|x-2| = 1
means all numbers x which are at a distance of 1 away from 2. What numbers are 1 away from 2? 1 and 3. 1 and 3 are the solutions to this equation. Hence this is not the equation you're looking for.

Answer 7

Second equation
|2x – 2| = 6

Divide both sides by 2 and you get
|x-1| = 3

What are the solutions of that equation? You want numbers that are a distance 3 away from 1.

Answer 8

so the solutions are -1 and 3?

Answer 9

No, 3 away from 1 is either -2 or 5. Do you see that?

Answer 10

i dont see how its 5? shouldn't it be 4?

Answer 11

need coffee! Yes, sorry, -2 or 4.

Answer 12

Third equation
|3x – 3| = 6

Divide both sides by 3
|x-1| = 2

What are the solutions of this equation?

Answer 13

ITS NOT -2 EITHER ITS -4

Answer 14

The solutions of
|x-1| = 3
are 1-3 = -2
and 1+3 = 4

Answer 15

ok so which one of the choices do you think it will be?

Answer 16

Third equation
|3x – 3| = 6

Divide both sides by 3
|x-1| = 2

What are the solutions of this equation?

Answer 17

HOW DO I FIND A SOLUTION?!?!?!?!

Answer 18

|x-1|=2 means numbers that are a distance 2 away from 1.
hence the solutions are
1-2
and
1+2

which are ... what?

Answer 19

so which one of the choices is it?

Answer 20

You're not following. What are the solutions to the third equation
|3x – 3| = 6

Answer 21

The solutions to that equation are the solutions to
|x-1| = 2
and the solutions to that equation are what?

Answer 22

I DONT KNOW!!! Ok, listen ive been working on this ALL day yesterday till 2am, got waken up today at 5am just to finish this. ive had enough. i have like no more brain power, and i dont have time for this. im bout to reach the deadline. so uhh, thanks for the help? i guess.

Answer 23

You are one step away from solving the problem.
|x-1| = 2
is the set of numbers which are a distance 2 away from 1.

Those two numbers are
1+2 = 3
and
1-2 = -1

----------

See the answer to your entire problem now?

Answer 24

no

Answer 25

You are told the solution to a particular equation is two numbers: -1 and 3.

The task is to find the equation which has -1 and 3 as its solution.

Didn't we just find the equation which has -1 and 3 as its solution?

Answer 26

Still there?