write the sentence as an absolute value inequality. I have no clue how to do this!
1 a number less than 4 units from 0
2. a number is more than 11 units from 8
3. half a number is at least 2 units from 20
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To write the given sentences as absolute value inequalities, we need to understand the definition of absolute value. The absolute value of a number is its distance from zero on the number line. It is always a positive value, regardless of whether the original number is positive or negative.
Now, let's convert each sentence into an absolute value inequality:
1. "A number less than 4 units from 0"
To represent this as an absolute value inequality, we start with the absolute value of the number and express it as less than 4:
|number| < 4
2. "A number is more than 11 units from 8"
For this sentence, we need to consider the absolute difference between the number and 8, and it should be greater than 11:
|number - 8| > 11
3. "Half a number is at least 2 units from 20"
In this case, we need to express the absolute value of half the number as being greater than or equal to 2 units away from 20:
|0.5 * number - 20| ≥ 2
In summary:
1. |number| < 4
2. |number - 8| > 11
3. |0.5 * number - 20| ≥ 2
Remember that these inequalities can be further simplified or solved depending on the context or specific requirements.