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# Write and solve an absolute value inequality

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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.

## Solving Absolute Value Inequalties with Greater Than 3 | arteensevilla.com

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. 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.

## How To Construct a Delta-Epsilon Proof

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. Negative 12 is less than 2 minus 5x, which is less than or equal to 7.

I want to do a problem that has just the less than and a less than or equal to.The absolute number of a number a is written as $$\left | a \right |$$ And represents the distance between a and 0 on a number line. An absolute value equation is an equation that contains an .

(We will discuss projectile motion using parametric equations here in the Parametric Equations section.). Note that the independent variable represents time, not distance; sometimes parabolas represent the distance on the $$x$$-axis and the height on the $$y$$-axis, and the shapes are arteensevilla.com versus distance would be the path or trajectory of the bouquet, as in the following problem.

After we’ve mastered how to solve Absolute Value Inequalities, we are going to learn how to write an equation or inequality involving absolute value to describe a graph or statement. Now, when solving Absolute Value Inequalities, we must never lose sight of the . Algebra > Absolute Value Equations and Inequalities > Solving Absolute Value Inequalties with Greater Than.

Always, silly! We can't even set this guy up to TRY to solve him. The answer is. previous. 1 2 3. Absolute Value Equations and Inequalities.

What's an Absolute Value? Solving Absolute Value Equations. Solving Absolute Value. Sep 03,  · This Algebra video tutorial explains how to solve inequalities that contain fractions and variables on both sides including absolute value function expressions.

Clear out the absolute value symbol using the rule and solve the linear inequality. Isolate the variable “ x ” in the middle by adding all sides by 6 and then dividing by 3 (coefficient of x).

The inequality symbol suggests that the solution are all values of x between -3 and 7, and also including the endpoints -3 and 7.

How to Solve Absolute Value Inequalities? (13 Surefire Examples!)