Absolute value equations have more than one solution because when the answer is in abs. value, it is positive, so there could be a negative answer and it would still be positive. For example |-5|=5 and |5|=5 as well.
4+|2x|=-1 would have no solution because you cannot have the equation equal a negative since the 2x is in absolute value.
Answer: Choice C) -1/3
The given line has a slope of -1/3 so anything parallel to that given line is also going to have an equal slope (of -1/3)
To find the slope of that line shown, notice how we drop down 1 unit and the move to the right 3 units when we go from the left point to the right point. Alternatively, you can use the slope formula m = (y2-y1)/(x2-x1) to get the same result.
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Use distributive method
5r - 50 = -51
Add 50
5r = -1
Divide by 5
r = -1/5