SOLUTION: how do i solve the equation? 3|x-4|=10 i no there are two solutions, 2/3 and 22/3, i know how to solve the equation to get 22/3 but i dont know how to get 2/3? How would i do

Algebra ->  Real-numbers -> SOLUTION: how do i solve the equation? 3|x-4|=10 i no there are two solutions, 2/3 and 22/3, i know how to solve the equation to get 22/3 but i dont know how to get 2/3? How would i do       Log On


   

Question 448102: how do i solve the equation?
3|x-4|=10
i no there are two solutions, 2/3 and 22/3, i know how to solve the equation to get 22/3 but i dont know how to get 2/3? How would i do this? Thanks for all your help!
Found 2 solutions by jim_thompson5910, ankor@dixie-net.com:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Divide both sides by 3 to get abs%28x-4%29=10%2F3


Now use the idea that abs%28x%29=y means x=y or x=-y to get the two equations


x-4=10%2F3 or x-4=-10%2F3


Solving the first equation gives you x=22%2F3, which you already know how to do.


Solve the second equation x-4=-10%2F3 to get



x-4=-10%2F3


x=-10%2F3%2B4


x=-10%2F3%2B4%283%2F3%29


x=-10%2F3%2B12%2F3


x=%28-10%2B12%29%2F3


x=2%2F3


So the other solution is x=2%2F3

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
3|x-4| = 10
Divide both sides by 3
|x-4| = 10%2F3
Remove absolutes, solve for two solutions
x - 4 = 10%2F3
x = 10%2F3 + 4
x = 10%2F3 + 12%2F3
x = 22%2F3
and
x - 4 = -10%2F3
x = -10%2F3 + 4
x = -10%2F3 + 12%2F3
x = 2%2F3