# Writing absolute value inequalities worksheet

### Absolute value equations and inequalities worksheet with answers

If, say, w was , minus is going to be negative 1. That translates to that, which translates to f of x greater than negative a and f of x less than a. In order for the leg to fit, it needs to be millimeters wide, allowing for a margin of error of 2. So we could write 7x needs to be one of these numbers. So I just want to-- you could memorize this if you want, but I really want you to think about this is just saying, OK, this has to evaluate, be less than a away from 0, this has to be more than a away from 0. This process can feel a bit weird, so I'll give a couple examples of how it works. You'll get 2x plus 63 is less than negative 5. So that means that f of x has to be less than positive a or greater than negative a. So in order to satisfy this thing in this absolute value sign, it has to be-- so the thing in the absolute value sign, which is 5x plus it has to be greater than negative 7 and it has to be less than 7, in order for its absolute value to be less than 7. Absolute value inequalities Video transcript I now want to solve some inequalities that also have absolute values in them. But 4 will not work, and neither will —4, because they are too far away from zero. These solutions must be written as two inequalities. And you really should visualize a number line when you do this, and you'll never get confused then. You have to be in this range.

If w is less thanit's going to be a negative number. Notice how the solution set is displayed on the thermometer.

That means that the absolute value of f of x, or f of x has to be less than a away from 0. Because the variable cannot be in both of the solution intervals and the same time.

## Absolute value equations and inequalities quiz answers

The number 2 will work, as will —2. The x - You get, in this case, x is greater than-- you don't have to swap the inequality, because we're dividing by a positive number-- negative 58 over 2 is negative 29, or, here, if you divide both sides by 2, or, x is less than negative Example 3 Solve each of the following. What do you get? That's the solution set right there. To start, I look at the endpoints.

Let's do it over here, too. You'll get 2x plus 63 is less than negative 5.

## Absolute value equations worksheet

So that means that f of x has to be less than positive a or greater than negative a. Section : Absolute Value Inequalities In the previous section we solved equations that contained absolute values. You subtract 3 from both sides. And, by the way, the correct conjunction is "or", not "and". That means that the absolute value of f of x, or f of x has to be less than a away from 0. In interval notation, it would be everything between negative 12 and positive 12, and not including those numbers. Like this. Let's do positive 21, and let's do a negative 21 here. Minus two and plus four are six units apart. Please tell us who you are Please start by selecting all of the fields. Regardless of direction, positive or negative, the distance between the two points is represented as a positive number or zero. However, the number 2.

See if we subtract-- let's just multiply everything by 7, just to get these denominators out of the way. Regardless of direction, positive or negative, the distance between the two points is represented as a positive number or zero.

So this, you could say, this could be all of the numbers where x is greater than negative So its absolute value is going to be greater than a.

DO NOT try to write this as one inequality.

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