# Writing absolute value inequalities graph

Then click the button and select "Solve for x" to compare your answer to Mathway's.

The dog can pull ahead up to the entire length of the leash, or lag behind until the leash tugs him along. What can she expect the graph of this inequality to look like?

But I think it lays a good foundation for the next few problems. So I want to adjust the inequality so it relates to —2.

In this inequality, they're asking me to find all the x-values that are less than three units away from zero in either direction, so the solution is going to be the set of all the points that are less than three units away from zero.

Let's say we have the absolute value of 2x-- let me do another one over here. B Two rays: one beginning at 0. Half of six is three.

## Absolute value inequalities calculator

The x is in the interval that satisfied both inequalities at the same time. And then we can just solve these. Even 3 and —3 won't work though they're right on the edge , because this is a "less than" but not equal to inequality. But 4 will not work, and neither will —4, because they are too far away from zero. And I could actually write it like this. We'll do several of these practice problems, so it really gets ingrained in your brain. The first step is to isolate the absolute value term on one side of the inequality. Let's say the absolute value of 5x plus 3 is less than 7. Affiliate Even when the inequalities are more complicated, the above pattern still holds. Let's do a couple more of these. But can an absolute value ever be negative, let alone be less than a negative? However, the number 2. This process can feel a bit weird, so I'll give a couple examples of how it works. 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. In other words, the dog can only be at a distance less than or equal to the length of the leash.

In a double inequality we require that both of the inequalities be satisfied simultaneously. You know, you take the absolute value of negative 6, that's only 6 away from 0.

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