# Write an absolute value equation that has 3 and 11 as its solution

Questions Eliciting Thinking Can you reread the first sentence of the second problem? A difference is described between two values. What are these two values? What is the difference? Compound inequalities Video transcript Let's do some compound inequality problems, and these are just inequality problems that have more than one set of constraints. You're going to see what I'm talking about in a second. So the first problem I have is negative 5 is less than or equal to x minus 4, which is also less than or equal to So we have two sets of constraints on the set of x's that satisfy these equations.

So we could rewrite this compound inequality as negative 5 has to be less than or equal to x minus 4, and x minus 4 needs to be less than or equal to And then we could solve each of these separately, and then we have to remember this "and" there to think about the solution set because it has to be things that satisfy this equation and this equation.

So let's solve each of them individually. So this one over here, we can add 4 to both sides of the equation. The left-hand side, negative 5 plus 4, is negative 1. Negative 1 is less than or equal to x, right? These 4's just cancel out here and you're just left with an x on this right-hand side.

So the left, this part right here, simplifies to x needs to be greater than or equal to negative 1 or negative 1 is less than or equal to x. So we can also write it like this. X needs to be greater than or equal to negative 1. I just swapped the sides. Now let's do this other condition here in green.

Let's add 4 to both sides of this equation. The left-hand side, we just get an x.

## Compound inequalities

And then the right-hand side, we get 13 plus 14, which is So we get x is less than or equal to So our two conditions, x has to be greater than or equal to negative 1 and less than or equal to So we could write this again as a compound inequality if we want.

We can say that the solution set, that x has to be less than or equal to 17 and greater than or equal to negative 1. It has to satisfy both of these conditions. So what would that look like on a number line? So let's put our number line right there. Let's say that this is You keep going down.

Maybe this is 0. I'm obviously skipping a bunch of stuff in between. Then we would have a negative 1 right there, maybe a negative 2. So x is greater than or equal to negative 1, so we would start at negative 1.

We're going to circle it in because we have a greater than or equal to. And then x is greater than that, but it has to be less than or equal to So it could be equal to 17 or less than So this right here is a solution set, everything that I've shaded in orange.

And if we wanted to write it in interval notation, it would be x is between negative 1 and 17, and it can also equal negative 1, so we put a bracket, and it can also equal So this is the interval notation for this compound inequality right there.

Let's do another one. Let me get a good problem here. Let's say that we have negative I'm going to change the problem a little bit from the one that I've found here.In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are metin2sell.com systems are referred to as quantum (mechanical) systems.

The equation is considered a central result in the study of quantum systems, and its derivation was a significant landmark in. Dec 15,  · Write an absolute value equation that has the given solutions.? 1) 1 and 5 2) 5 and 11 3) -2 and 8.

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Follow Write an absolute value inequality whose solution set is given by the interval notation:? How to write an absolute value equation? More metin2sell.com: Resolved. 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. Write an absolute value equation that has -3 and 15 as its solutions.

The absolute value of a difference between two numbers is how far the two numbera are apart on a number line. This is the currently selected item. Worked example: absolute value equation with two solutions Worked example: absolute value equations with one solution Worked example: absolute value equations with no solution Let's do some equations that deal with absolute values.

And just as a bit of a review.

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. In this section we solve linear first order differential equations, i.e. differential equations in the form y' + p(t) y = g(t). We give an in depth overview of the process used to solve this type of differential equation as well as a derivation of the formula needed for the integrating factor used in the solution process. In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are metin2sell.com systems are referred to as quantum (mechanical) systems. The equation is considered a central result in the study of quantum systems, and its derivation was a significant landmark in.

Write an absolute value equation that has the solutions x=2 and x=9 Get the answers you need, now!

Worked example: absolute value equations with no solution (video) | Khan Academy