Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval.
\[ |2x-1|+|2x|=|1-x|-|x+4| \]
Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are negative on this interval.
\[ |5-x|-|x+3|=|x+1| \]
Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval.
\[ |x+3|+|2x|=|x-1| \]
Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval.
\[ |2x+4|+|-x+1|=2x \]
Find the set of the zero points of all the absolute values from the equation.
\[ |-x+1|=|3x+9|-|2x|\]
(The zero point is the value of \( x \) for which the absolute value equals zero.)
Find the sum of the zero points of all the absolute-value expressions of the equation.
\[ |x-3|=|x+9|-|-2+x| \]
(The zero point is the value of \( x \) for which the absolute-value expression equals zero.)