For example, the number of squirts must divide evenly into the number of cylinders, etc. When in doubt, trust the calculator used in MegaTune.
Absolute value equations Video transcript We're asked to solve for x. Let me just rewrite this equation so that the absolute values really pop out.
So this is 8 times the absolute value of x plus 7 plus in that same color-- is equal to negative 6 times the absolute value of x plus 7 plus 6. Now the key here-- at first it looks kind of daunting. It's this complex equation. You have these absolute values in it.
But the way to think about this is if you could solve for the absolute value expression, you could then-- it then turns into a much simpler problem, then you can take it from there.
So you could almost treat this expression-- the absolute value of x plus 7, you can just treat it as a variable, and then once you solve for that, it becomes a simpler absolute value problem.
So let's try to do that. Let's try to solve for not x first. We're just going to solve for the absolute value of x plus 7. You'll see what I mean. So I want to get all of the absolute values of x plus 7 on the left-hand side, so I want to get rid of this one on the right-hand side.
Easiest way to get rid of it is to add 6 times the absolute value of x plus 7 to the right-hand side. We can't, of course, only do that to the right-hand side. If these two things are equal and we are being told that they are, then if you add something on this side, the only way that the equality will hold is if you still do it on the left-hand side.
So let's do that, so plus 6 times the absolute value of x plus 7. And I want to get all of these constant terms on to the right-hand side. So I want to get rid of this positive 4.
Easiest way is to subtract 4 right over there, but if we do it on the left-hand side, we have to do it on the right-hand side as well. And so what does this get us? So our left-hand side, if I have 8 of something-- and in this case the something is absolute values of x plus 7's-- but if I have 8 of something and I add 6 of that same something, I now have 14 of that something.
So that's going to be 14 absolute values of x plus 7, 14 times the absolute value of x plus 7. The 4 and the negative 4 cancel out, and that was intentional.
The negative 6 and the 6 x plus 7's cancel out, or absolute values of x plus 7's cancel out, and that was intentional. And then we're left with 6 minus 4, which is just 2. So that's going to be equal to 2. Now just as promised, we want to solve for the absolute value of x plus 7, so let's divide both sides by 14 to get rid of that coefficient there, or that factor, or whatever you want to call it, the thing that's multiplying the absolute value of x plus 7.
So just as promised, we've now solved for the absolute value of x plus 7, but we really need to solve for x. So how can we reason through this?
And just think about that for a second.
So that's how we got this. So now let's just solve for x. So that's one possibility for x. We're just subtracting 7 from both sides.In chemistry, pH (/ p iː ˈ eɪ tʃ /) is a logarithmic scale used to specify the acidity or basicity of an aqueous srmvision.com is approximately the negative of the base 10 logarithm of the molar concentration, measured in units of moles per liter, of hydrogen srmvision.com precisely it is the negative of the base 10 logarithm of the activity of the hydrogen ion.
2 Solving Absolute Value Equations So, the equation has no solution. EXAMPLE 1 Solving Absolute Value Equations Solve the equation.
Graph the solutions. 1. Write an absolute value equation to ﬁ nd the minimum and maximum calorie intake per day for this program.
This absolute value equation is set equal to minus 8, a negative number. By definition, the absolute value of an expression can never be negative. Hence, this equation has no solution. The absolute value always returns a positive value, so it is impossible for the absolute value to equal a negative value.
At this point, we notice that this equation has no solutions. Q & A. Nernst Equation. The Nernst equation is an important relation which is used to determine reaction equilibrium constants and concentration potentials as well as to calculate the minimum energy required in electrodialysis as will be shown later.
Simply knowing how to take a linear equation and graph it is only half of the battle. You should also be able to come up with the equation if you're given the right information.