Question

I WILL GIVE MEDAL just help me please
what are the solutions to this equation|x-10|-4=2x

Answer 1

the absolute value sign means we need to solve for two cases, one where (x-10) is positive and one where (x-10) is negative

so we get:

1. x - 10 - 4 = 2x
2. -(x-10) - 4 = 2x

solve each equation for x

Answer 2

1. x - 10 - 4 = 2x
do i add 4 with -4 and 2x?

Answer 3

add 4 to both sides of the equal sign and tell me what you get

Answer 4

1. x - 10 - 4 = 2x
+4 +4
x-10=2x+4 is it like that?

Answer 5

yes, now keep going

Answer 6

Why not x - 10 - 4 = 2x -> x - 14 = 2x ?

Answer 7

^ that works, too

Answer 8

Then subtract x from both sides

Answer 9

don't worry about that equation as it doesn't have a valid solution

solve the other equation

Answer 10

im still confuse with the first one..

Answer 11

ok, we can pick up where you left off

x-10=2x+4

now add 10 to both sides

Answer 12

x=2x+14 is it like that?

Answer 13

right, now subtract 2x from both sides

Answer 14

x=2x+14
-2x -2x
x=12x

Answer 15

not quite, remember that you can't combine 14 since there's no x attached to it

x - 2x = ?

Answer 16

oh ok so its
x-2x=14-2x

Answer 17

almost

x-2x = 2x+14-2x

now keep going

x - 2x = ?

Answer 18

12

Answer 19

nope

1-2 = ?

Answer 20

-1

Answer 21

right, so if 1-2 = -1, what does x - 2x = ?

Answer 22

-x

Answer 23

correcto, now we have

-x = 2x+14-2x

what is 2x+14-2x?

Answer 24

im not sure

Answer 25

hint: 2x - 2x = ?

Answer 26

0

Answer 27

good, so what is 2x+14-2x?

Answer 28

0

Answer 29

not quite...

2x+14-2x = 2x-2x+14 = ?

Answer 30

It may be easier if it's re written as 2x - 2x + 14 = ?

Answer 31

@Vocaloid never mind I didn't realize you wrote the same thing

Answer 32

12

Answer 33

nope, not quite..

2x - 2x = 0

2x - 2x + 14 = ?

Answer 34

2x - 2x + 14 => 0 + 14

Answer 35

14

Answer 36

right, that gives us

-x = 14, which makes x = -14. (this solution doesn't quite work, like campbell mentioned, we'll see why later)

now on to the second equation ~

Answer 37

-(x-10) - 4 = 2x

Answer 38

-(x-10) - 4 = 2x
-x+10-4=2x

Answer 39

good, keep going

10-4 = ?

Answer 40

6

Answer 41

good, that gives us

-x + 6 = 2x

now add x to each side

Answer 42

-x + 6 = 2x
+x +x
-x+6x+2x+x

Answer 43

not quite, remember that you can't combine numbers and variables

-x + x + 6 = 2x + x

Answer 44

now keep going

-x + x + 6 = ?

Answer 45

6

Answer 46

excellent! now, x + 2x = ?

Answer 47

2x

Answer 48

nope, here's a hint:

1 + 2 = 3
x + 2x = ?

Answer 49

3x

Answer 50

good, now we have

3x = 6

now divide both sides by 3

Answer 51

x=2

Answer 52

good, we're almost done

after solving the two equations we have

x = -14 and x = 2

our next step is to substitute back into the original equation to see which ones work and which ones don't

when we plug in x = -14, we get

|x-10|-4=2x
|-14-10|-4 = 2(-14)
|-24|-4 = -28
24 - 4 = -28
20 = -28 (this is not true, so x = -14 is not our solution)

Answer 53

next, we try x = 2

|x-10|-4=2x
|2-10| -4 = 2(2)
|-8| - 4 = 4
8 - 4 = 4
4 = 4

this is true, so x = 2 is our only solution

Answer 54

ohh ok

Answer 55

so it's x=-14 and x=2

Answer 56

i would say it is because of the work that you guys did up above but if not i will go back through it with you.