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

- anonymous

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

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- schrodinger

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- Vocaloid

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

- anonymous

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

- Vocaloid

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

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## More answers

- anonymous

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

- Vocaloid

yes, now keep going

- anonymous

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

- Vocaloid

^ that works, too

- anonymous

Then subtract x from both sides

- campbell_st

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

- anonymous

im still confuse with the first one..

- Vocaloid

ok, we can pick up where you left off
x-10=2x+4
now add 10 to both sides

- anonymous

x=2x+14 is it like that?

- Vocaloid

right, now subtract 2x from both sides

- anonymous

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

- Vocaloid

not quite, remember that you can't combine 14 since there's no x attached to it
x - 2x = ?

- anonymous

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

- Vocaloid

almost
x-2x = 2x+14-2x
now keep going
x - 2x = ?

- anonymous

12

- Vocaloid

nope
1-2 = ?

- anonymous

-1

- Vocaloid

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

- anonymous

-x

- Vocaloid

correcto, now we have
-x = 2x+14-2x
what is 2x+14-2x?

- anonymous

im not sure

- Vocaloid

hint: 2x - 2x = ?

- anonymous

0

- Vocaloid

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

- anonymous

0

- Vocaloid

not quite...
2x+14-2x = 2x-2x+14 = ?

- anonymous

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

- anonymous

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

- anonymous

12

- Vocaloid

nope, not quite..
2x - 2x = 0
2x - 2x + 14 = ?

- anonymous

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

- anonymous

14

- Vocaloid

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 ~

- Vocaloid

-(x-10) - 4 = 2x

- anonymous

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

- Vocaloid

good, keep going
10-4 = ?

- anonymous

6

- Vocaloid

good, that gives us
-x + 6 = 2x
now add x to each side

- anonymous

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

- Vocaloid

not quite, remember that you can't combine numbers and variables
-x + x + 6 = 2x + x

- Vocaloid

now keep going
-x + x + 6 = ?

- anonymous

6

- Vocaloid

excellent! now, x + 2x = ?

- anonymous

2x

- Vocaloid

nope, here's a hint:
1 + 2 = 3
x + 2x = ?

- anonymous

3x

- Vocaloid

good, now we have
3x = 6
now divide both sides by 3

- anonymous

x=2

- Vocaloid

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)

- Vocaloid

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

- anonymous

ohh ok

- anonymous

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

- dm91

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.

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