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 know the answers (got from another source) but I don't know how to get them.
the first one is |x|< 2
the second one is |x+4|< 1
Please help me ASAP!!! This homework is due tomorrow 12/15. Thanks!
All number less than 2 from zero means all numbers from -2 to +2. Let x be one of the numbers in that range. It should be clear that |x| < 2 means the same thing as being between -2 and +2.
Similar reasoning applies to the second problem, where the range is -5 to -3. "x+4" is the distance of a number x from -4.
To write an absolute value inequality that represents a set of numbers, you need to think about the distance of those numbers from a specific point.
For the first problem, "all real numbers less than 2 units from 0," you want to represent all numbers that are within 2 units from 0. In this case, the distance from 0 to any number will be the absolute value of that number, denoted as |x|.
So, if you want all numbers less than 2 units from 0, you can write the inequality as |x| < 2. This means that the absolute value of x should be less than 2, indicating that x is within 2 units of 0.
For the second problem, "all real numbers less than 1 unit from -4," you need to consider the distance between any number (x) and -4. This distance can be represented as |x+4| since x + 4 gives the value of x's position relative to -4.
For all numbers less than 1 unit from -4, you can write the inequality as |x + 4| < 1. This implies that the absolute value of the expression x + 4 should be less than 1, indicating that x is within 1 unit of -4.
In summary, to write an absolute value inequality that represents a set of numbers, you should choose a variable (like x) to represent the numbers in the range, determine the distance of those numbers from a reference point, and write the inequality using absolute value notation.