SOLUTION: |6x-3|=7

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Question 730560: |6x-3|=7
Answer by hoomanc(14) About Me  (Show Source):
You can put this solution on YOUR website!
the absolute value function is always something like this:
f(X)=|g(x)| if you want to remove absolute sign and write a simple model of function instead it's as follow:
f(X)=|g(x)| is equal to two different function all the time:
1) for X%3C0 >>> f%28X%29=-1%2Ag%28x%29 and
2) for X%3E0 >>> f%28X%29=+1%2Ag%28x%29
so in this case:
f%28X%29=7 and g%28x%29=6x-3
so,
1) for X%3C0 >>> 7=-1%2A%286x-3%29 >>> 7=-6x%2B3%29 >>>4=-6x%29 >> X=-2%2F3%29
since you assumed that X should be negative at the first place X%3C0 and you find X=-2%2F3%29 it is a valid answer, otherwise if it was not negative, it was not acceptable.
2) for X%3E0 >>> f%28X%29=+1%2Ag%28x%29 >>> 7=6x-3%29 >>> 10=6x%29 >>> X=5%2F3%29 again since it's a positive as we assumed for this case it is acceptable.
in conclusion the answers are : -2%2F3 and 5%2F3