How to write and solve an absolute value equation with no solutions
And likewise, I want to get all my constant terms, I want to get this 4 out of the left-hand side. Therefore, there is no solution for either of these.
So there's no x that you could find that's somehow-- you put it there, you add 10, you take the absolute value of it, you're actually getting a negative value. And now let's see what we end up with. Example 2 Solve each of the following.
The solution for each of these is then all real numbers. If these two things are equal, and if I want to keep them equal, if I subtract 6 from the right-hand side, I've got to subtract-- or if I subtract 6 times the absolute value of x plus 10 from the right-hand side, I have to subtract the same thing from the left-hand side.
The first equation will set the quantity inside the bars equal to the number on the other side of the equal sign; the second equation will set the quantity inside the bars equal to the opposite of the number on the other side.
Write two equations without absolute values. And I'll put some exclamation marks there for emphasis. If you answered no, then go on to step 3.
Absolute value equations
Same way, you have 4 of this expression, you take away 6 of this expression, you now have negative 2 of this expression. You might realize, everything we've done so far is just treating this red expression as almost just like a variable, and we're going to solve for that red expression and then take it from there. Doesn't matter what x you put in there, when you take its absolute value, you're going to get a value that's greater than or equal to 0. Practice Problems These are practice problems to help bring you to the next level. There is only one solution to this absolute value equation: 2. So on the left-hand side, the 4 minus 4, that's 0. Is the number on the other side of the equation negative? Let me write it a little bit neater. So this thing right over here is definitely going to be greater than or equal to 0. So we're going to have minus 6 times the absolute value of x plus Negative 2 of the absolute value of x plus Write two equations without absolute values.
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