Write an absolute value inequality from a graph

Write an absolute value inequality for the graph below calculator

Since this is a "less than" absolute-value inequality, my first step is to clear the absolute value according to the "less than" pattern. So the actual solution set to this equation-- let me draw a number line-- let's say that's 0, that's 3, that is negative 3. I have negative Well, all of these negative numbers that are less than negative 21, when you take their absolute value, when you get rid of the negative sign, or when you find their distance from 0, they're all going to be greater than Half of six is three. Let's do positive 21, and let's do a negative 21 here. In order for the leg to fit, it needs to be millimeters wide, allowing for a margin of error of 2. So this means that w minus has to be less than 2. But I think it lays a good foundation for the next few problems. B Two rays: one beginning at 0. And we're done. To start, I look at the endpoints.

In order for the leg to fit, it needs to be millimeters wide, allowing for a margin of error of 2. Because if it's less than negative 21, when you take its absolute value, it's going to be more than 21 away from 0.

How to solve inequalities with absolute values on both sides

In interval notation, it would be everything between negative 12 and positive 12, and not including those numbers. Or less than or equal to negative 3. If our absolute value is greater than or equal to 21, that means that what's inside the absolute value has to be either just straight up greater than the positive 21, or less than negative So I can convert my last line above to: x — So we want all of the numbers, so whatever this thing is, that are greater than or equal to You know, you take the absolute value of negative 6, that's only 6 away from 0. In other words, the solution will be two separate sections: one section being all the points more than two units from zero off to the left, and the other section being all the points more than two units from zero off to the right. And I could actually write it like this. Writing inequalities algebra Absolute value inequalities Video transcript A carpenter is using a lathe to shape the final leg of a hand-crafted table. And then we can just solve these. We're doing this case right here. If the absolute value of the variable is more than the constant term, then the resulting graph will be two rays heading to infinity in opposite directions. Let's do positive 21, and let's do a negative 21 here. But once you have this set up, and this just becomes a compound inequality, divide both sides of this equation by 7, you get x is less than or equal to negative 3. If we add to both sides of these equations, if you add and we can actually do both of them simultaneously-- let's add on this side, too, what do we get?

And you really should visualize a number line when you do this, and you'll never get confused then. Or we could write it like this, x is less than 12, and is greater than negative Hopefully that make sense.

absolute value inequalities and or or

Since this is a "less than" absolute-value inequality, my first step is to clear the absolute value according to the "less than" pattern. If we add to both sides of these equations, if you add and we can actually do both of them simultaneously-- let's add on this side, too, what do we get?

absolute value inequalities calculator

They're more than 21 away from 0. And I really want you to understand this.

double absolute value inequalities
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Absolute value inequalities word problem (video)