Scientists suggest spacetime has no time dimension April 25, by Lisa Zyga, Phys. But some researchers theorize that this Newtonian idea of time as an absolute quantity that flows on its own, along with the idea that time is the fourth dimension of spacetime, are incorrect.
Absolute value equations Video transcript So we're asked to solve for x, and we have this equation with absolute values in it. So it's 4 times the absolute value of x plus 10 plus 4 is equal to 6 times the absolute value of x plus 10 plus And at first, this looks really daunting, but the key is to just solve for this absolute value expression and then go from there.
Let me just rewrite it so that the absolute value expression really jumps out. So this is 4 times the absolute value of x plus 10 plus 4 is equal to 6 times the absolute value of x plus 10 plus So let's get all of the absolute values of x plus 10 on the left-hand side.
So I want to get rid of the 6 times the absolute value of x plus 10 on the right. Well, how would I do that? Well, I could subtract 6 times the absolute value of x plus 10 from the right, but we've already seen this multiple times.
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.
So we're going to have minus 6 times the absolute value of x plus And likewise, I want to get all my constant terms, I want to get this 4 out of the left-hand side.
So let me subtract 4 from the left, and then I have to also do it on the right, otherwise my equality wouldn't hold. And now let's see what we end up with.
So on the left-hand side, the 4 minus 4, that's 0. You have 4 of something minus 6 of something, that means you're going to end up with negative 2 of that something. Negative 2 of the absolute value of x plus Remember, this might seem a little confusing, but remember, if you had 4 apples and you subtract 6 apples, you now have negative 2 apples, I guess you owe someone the apples.
Same way, you have 4 of this expression, you take away 6 of this expression, you now have negative 2 of this expression. Let me write it a little bit neater. So it's negative 2 times the absolute value of x plus 10 is equal to, well the whole point of this, of the 6 times the absolute value of x plus 10 minus 6 times the absolute value of x plus 10 is to make those cancel out, and then you have 10 minus 4, which is equal to 6.
Now, we want to solve for the absolute value of x plus So let's get rid of this negative 2, and we can do that by dividing both sides by negative 2. 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.
So negative 2 divided by negative 2 is 1. So we get the absolute value of x plus 10 is equal to negative 3.
Now, this gets us to a very interesting situation. You might say maybe this could be the positive version or the negative, but remember, absolute value is always non-negative. If you took the absolute value of 0, you would get 0. But the absolute value of anything else is going to be positive. So this thing right over here is definitely going to be greater than or equal to 0.
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. 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.
So this right over here has absolutely no solution. And I'll put some exclamation marks there for emphasis.a. An extraneous solution is an irrational solution to an algebraic equation. b. An extraneous solution is an approximate solution to an algebraic equation.
c. An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation. d. Aug 01, · Learn how to solve absolute value inequalities.
Absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2.
Parametric Equations in the Graphing Calculator. We can graph the set of parametric equations above by using a graphing calculator.
First change the MODE from FUNCTION to PARAMETRIC, and enter the equations for X and Y in “Y =”.. For the WINDOW, you can put in the min and max values for \(t\), and also the min and max values for \(x\) and \(y\) if you want to.
Geoff Haselhurst. Below you will find some of my favourite philosophy quotes, a summary of my history, and on the side of this page links to the main philosophy, physics, metaphysics, evolution, education and politics articles that I have written.
Section Solving Exponential Equations. Now that we’ve seen the definitions of exponential and logarithm functions we need to start thinking about how to solve equations involving them. Absolute value equations have two solutions. Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets.