 In this video, we provide the solution to question number two from the practice exam number two for math 1050. We're given this absolute value equation. The absolute value of two sevenths x plus three fourths is all equal to one and we need to solve this equation. Well, whenever you have an absolute value equal to something, we have to check the sign on the other side. If you have absolute value equal to some negative number like negative two, you'd end up with no solution. If you have absolute value equal to zero, you'd only end up with one solution in that situation. So we would handle those exceptional cases if they occurred. In this situation, we just have absolute value is equal to a positive one. And so to remove the absolute value, we have to consider both the positive and negative case. So we get two sevenths x plus three fourths is equal to plus or minus one, right? I can actually consider both of these cases in tandem here. We're going to subtract three fourths from both sides of the equation. This then gives us two sevenths x is equal to negative three fourths plus or minus one, for which as you do have to ultimately add these together or subtract them, I'm going to rewrite the one as a four over four. Thus this becomes negative three plus or minus four over four. Again, just for convenience later on. To solve for x, then we would times both sides by seven halves, the reciprocal of the coefficient there. So we do that on the other side as well, seven halves like so. And so we end up with seven times negative three plus or minus four all over four times two is eight. Now we're at the point which we really can't go any further without actually considering the two cases. So we have these two cases. We have the addition in the subtraction of seven times negative three plus four over eight, and then we have seven times negative three minus four all over eight. In the first case three, that is four minus three, that can be one, one times seven is seven. So we end up with a seven eighths as one of the solutions. And then on the second one, you're going to get negative three minus four, which is a negative seven, like so, seven times negative seven gives us a negative 49 still over eight. And so we see that the correct answer then would be choice E.