# Writing absolute value inequalities from word problems

### Absolute value inequalities word problems worksheet with answers

In order for the leg to fit, it needs to be millimeters wide, allowing for a margin of error of 2. We get the first equation by just taking away the absolute value sign away on the left. If w is going to be larger than , let's say it's , then this difference is going to be 1 millimeter, we were over by 1 millimeter. But we just care about the absolute margin. So let's solve each of these. And that's the range. And I'm assuming less than-- they're saying a margin of error of 2. The left-hand side of this equation just becomes a w-- these cancel out-- is less than or equal to plus 2. We have written an absolute value inequality that models this relationship. Now, they want us to write an absolute value inequality that models this relationship, and then find the range of widths that the table leg can be. 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? Or it has to be greater than or equal to, or we could say Simplify with a common denominator. If, say, w was , minus is going to be negative 1.

And I'm assuming less than-- they're saying a margin of error of 2. We get the first equation by just taking away the absolute value sign away on the left.

## Absolute value inequalities word problems worksheet with answers

We have written an absolute value inequality that models this relationship. If, say, w was , minus is going to be negative 1. So let me write this down. This is essentially how much of an error did we make, right? In order for the leg to fit, it needs to be millimeters wide, allowing for a margin of error of 2. Or it has to be greater than or equal to, or we could say And on this side of the equation-- this cancels out-- we just have a w is greater than or equal to negative 2. The width has to be less than or equal to And that's the range. We can write it like this. You can also put the equation in your graphing calculator to check your answers! A lathe is this carpentry tool that spins things around, and so it can be used to make things that are, I guess you could say, almost cylindrical in shape, like a leg for a table or something like that. So we just really care about the absolute value of the difference between w and If w is less than , it's going to be a negative number.

We have written an absolute value inequality that models this relationship. The left-hand side of this equation just becomes a w-- these cancel out-- is less than or equal to plus 2. Even with the absolute value, we can set each factor to 0, so we get —4 and 1 as critical values.

## Absolute value inequalities word problems kuta

If, say, w was , minus is going to be negative 1. Now, they want us to write an absolute value inequality that models this relationship, and then find the range of widths that the table leg can be. So we just really care about the absolute value of the difference between w and All we're saying is look, this right here is the difference between the actual width of our leg and Then we check each interval with random points to see if the factored form of the quadratic is positive or negative, making sure we include the absolute value. The width has to be less than or equal to And I really want you to understand this. This tells us, how much of an error did we make? Or it has to be greater than or equal to, or we could say

The width has to be less than or equal to And all we care is that error, that absolute error, has to be a less than 2. So if we were to take the difference between w andwhat is this?

Then, set each absolute value to 0 to get boundary points, where the absolute values turn from negative to positive, or positive to negative. You can also put the equation in your graphing calculator to check your answers!

So let me write this down. Now draw number lines for each absolute value, and then for the whole equation above. So the width of our leg has to be greater than So this means that w minus has to be less than 2.

Now we have to separate the equations.

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