I didn't get how to do the problem. In my book it says to choose a variable and write an absolute value inequality that represents each set of numbers. Here are the problems I had--
all real numbers less than 2 units from 0
all real numbers less than 1 unit from -4
I need to write an inequality for the two problems. Please explain how to do this. I need to know ASAP! This homework is due tomorrow 12/15.
I'm sorry I forgot to add that I know the answers I just don't know how to get them.
the first one is |x|< 2
the second one is |x+4|< 1
Does anybody know how to get the answer? I'm sorry I didn't say that earlier. :-)
To solve these problems, you are asked to write absolute value inequalities given a specific set of numbers or conditions. Here's how to approach each problem:
1) "All real numbers less than 2 units from 0":
To start, let's choose the variable x to represent the numbers. The phrase "less than 2 units from 0" refers to the distance of x from 0. Since absolute value represents distance, we can write the inequality as:
|x| < 2
The absolute value of x should be less than 2. In other words, x must be within 2 units away from 0 (on either side). This inequality represents all real numbers that are closer to 0 than a distance of 2 units.
2) "All real numbers less than 1 unit from -4":
Again, let's choose x as the variable representing the numbers. The phrase "less than 1 unit from -4" implies that the distance between x and -4 should be less than 1 unit. Since the variable x is being compared to -4, we need to consider the absolute value of the expression x+4. Therefore, we can write the inequality as:
|x+4| < 1
The absolute value of x+4 should be less than 1. This represents all real numbers that are closer to -4 than a distance of 1 unit.
Please note that the answers you provided are correct. To solve these types of problems in general, it is essential to understand the meaning of the given conditions and how they relate to the absolute value. In this case, the absolute value represents the distance between a specific number (-4 or 0) and the variable (x).