Absolute Value Equations - Problem 4
To solve an absolute value equation, first isolate the absolute value equation to see how many, if any, solutions there will be. Remember that if the absolute value quantity is equal to a negative number, then there is no solution to the equation since an absolute value cannot equal a negative number. The first thing to do when solving an absolute value equation is to isolate the absolute value quantity using the same rules that apply to isolating the variable in an equation. In other words, eliminate everything else on the same side of the equal sign except for the absolute value quantity using inverse operations. If the result is that the absolute value quantity is equal to a negative number, then the equation has no solution. Absolute value refers to the distance a number is from 0 and a distance will always have a positive value.
When you're solving absolute value equations, keep in your back of your head that the first thing you want to do is to get the absolute value piece isolated. You want that piece all by itself. Like for example I need to get rid of this plus 10 before I can do any solving.
The opposite of plus 10 is to subtract 10 from both sides so I'll have 2x plus 1 and the absolute value is equal to the -7. Many students would continue, they would split the problem they'll be going along, you guys this is like a special problem.
Absolute value of something is equal to a negative number in this problem. Keep in mind absolute value means distance. You can't have a negative distance this doesn't make sense, this problem has no solution. It's like an impossible problem. There is no number that I could put in there for x and I would get answer of -7 when I absolute value it, because absolute value means like making the quantity positive. Nothing I would plug in there will give me absolute value equal to -7.
This problem is kind of like a present it's done there is no solution. There is no way I would have known without looking at this original problem but the way you can tell you'll always know there is no solution is if you have an absolute value all by itself isolated equal to a negative value.