Question

Step 1: |x - 2| + 3 = 7
Step 2: |x - 2| = 7 - 3
Step 3: |x - 2| = 4

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

x + 2 = -4

-x – 2 = 4

x + 2 = 4

x - 2 = -4

Answer 1

@pgpilot326
since the absolute value cant be negative would that be x+2=4?

Answer 2

so think |something|=4 what can that something possibly be?

Answer 3

in other words, which numbers are 4 away from 0?

Answer 4

x - 2 could be equal to 4 or -4

Answer 5

in both cases the absolute value is 4

Answer 6

so which option is correct?

Answer 7

c?

Answer 8

no

Answer 9

as i said x - 2 could be equal to -4

Answer 10

so x-2=-4

Answer 11

yes
whats inside the modulus lines can be positive or negative

Answer 12

there are 2 roots in the solution set x = 2 and x = 6

Answer 13

sorry x = -2

Answer 14

if @cwrw238 isn't explaining it to your satisfaction, let me know and I'm happy to help

Answer 15

im really confused i thought the numbers inside the symbol couldnt be a negative?

Answer 16

no they can be - its the modulus lines which tell you to take the absolute value t(he positive value)

Answer 17

okay thanks i kind of get it

Answer 18

| -4 | = 4
and

| 4 | = 4

Answer 19

so |x-2| is |x+2|

Answer 20

An easier way to remember this is;

|x - 2| = 4 ==> x - 2 = 4 and x - 2 = -4

Answer 21

whatever 'comes out' of the modulus lines becomes positive
thats not a mathematically correct way of explaining it but it might help you

Answer 22

is the answer to this one x-2=-4?

Answer 23

yes

Answer 24

equally x - 2 = 4 could be the next step

Answer 25

lets do the full solution for you

|x - 2| + 3 = 7
|x - 2| = 7 - 3
|x - 2| = 4
x - 2 = -4
x = -2

and

x - 2 = 4
x = 6

so the solution set is {-2,6}


or if you like x = -2 or x = 6

Answer 26

ok that cleared it up a little bit howd the 4 become negative though?

Answer 27

well x - 2 ( the part inside the modulus lines) can be negative or positive
right?

Answer 28

right

Answer 29

can you help me with one more i have a idea of what the answer is

Answer 30

- I can see where you are getting a bit confused
the -4 becomes negative because the x -2 can be negative

if you find it easier do it this way

we have either (x -2) or -(x - 2) = 4

so its x - 2 = 4 so x = 6
or

-(x -2) = 4
-x + 2 = 4
-x = 2
x = -2

but the algebra is a bit harder this way

Answer 31

okay thanks that makes it easier

Answer 32

right - you are making the bit inside the lines neagtive instead of the 4
- both give same answer

Answer 33

you have one more - i have about 15 minutes before i have to go

Answer 34

The table shows the solution to the equation |2x – 3| - 1 = 2:

Step 1 |2x – 3| = 2 + 1
Step 2 |2x – 3| = 3
Step 3 2x – 3 = 3 or 2x + 3 = 3
Step 4 2x = 6 or 2x = 0
Step 5 x = 3 or x = 0


Which is the first incorrect step

Answer 35

im thinking step 3

Answer 36

yes - they have changed 2x - 3 to 2x+ 3 - that is wrong
it should read
2x -3 = 3 or 2x - 3 = -3

or

2x - 3 = 3 or -(2x - 3) = 3

Answer 37

I think you've understood it now

Answer 38

yes i do thanks for the help

Answer 39

yw