Absolute values are a way of finding a distant from zero, which means there will be 2 answers; one will be positive, and the other will be negative.
[tex]|3x-4|=5 and |3x-4|=—5 [/tex] Because you need 2 answers, you have to make 5 positive and negative.
Another way to write this equation would be...
5=|3x-4|=—5
Now lets continue...
5=3x-4=—5
Add 4 to both sides...
9=3x=—1
Now divide by 3...
3=x=[tex]-
\frac{1}{3} [/tex]
So the solution is...
X={[tex] -\frac{1}{3} [/tex], 3}
