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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
1. x - 10 - 4 = 2x do i add 4 with -4 and 2x?
add 4 to both sides of the equal sign and tell me what you get
1. x - 10 - 4 = 2x +4 +4 x-10=2x+4 is it like that?
yes, now keep going
Why not x - 10 - 4 = 2x -> x - 14 = 2x ?
^ that works, too
Then subtract x from both sides
don't worry about that equation as it doesn't have a valid solution solve the other equation
im still confuse with the first one..
ok, we can pick up where you left off x-10=2x+4 now add 10 to both sides
x=2x+14 is it like that?
right, now subtract 2x from both sides
x=2x+14 -2x -2x x=12x
not quite, remember that you can't combine 14 since there's no x attached to it x - 2x = ?
oh ok so its x-2x=14-2x
almost x-2x = 2x+14-2x now keep going x - 2x = ?
nope 1-2 = ?
right, so if 1-2 = -1, what does x - 2x = ?
correcto, now we have -x = 2x+14-2x what is 2x+14-2x?
im not sure
hint: 2x - 2x = ?
good, so what is 2x+14-2x?
not quite... 2x+14-2x = 2x-2x+14 = ?
It may be easier if it's re written as 2x - 2x + 14 = ?
@Vocaloid never mind I didn't realize you wrote the same thing
nope, not quite.. 2x - 2x = 0 2x - 2x + 14 = ?
2x - 2x + 14 => 0 + 14
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 ~
-(x-10) - 4 = 2x
-(x-10) - 4 = 2x -x+10-4=2x
good, keep going 10-4 = ?
good, that gives us -x + 6 = 2x now add x to each side
-x + 6 = 2x +x +x -x+6x+2x+x
not quite, remember that you can't combine numbers and variables -x + x + 6 = 2x + x
now keep going -x + x + 6 = ?
excellent! now, x + 2x = ?
nope, here's a hint: 1 + 2 = 3 x + 2x = ?
good, now we have 3x = 6 now divide both sides by 3
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)
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
so it's x=-14 and x=2
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.