How would I find an absolute value inequality which x is less than or equal to 6 or x is greater than or equal to 10?
To find the absolute value inequality, you would start by breaking down the given conditions into two separate inequalities.
The first condition, "x is less than or equal to 6," can be expressed as:
x ≤ 6.
The second condition, "x is greater than or equal to 10," can be expressed as:
x ≥ 10.
Now, to combine these two inequalities into a single absolute value inequality, you can use the logical connector "or." This means that either one of the conditions must be true.
So, the absolute value inequality would be:
|x - a| ≤ b, where a represents the midpoint between the two conditions (6 and 10), and b represents the maximum distance from the midpoint to either condition.
First, find the midpoint:
a = (6 + 10) / 2 = 16 / 2 = 8.
Next, find the maximum distance from the midpoint to either condition:
b = |6 - 8| = |-2| = 2.
Finally, combine the results into the absolute value inequality:
|x - 8| ≤ 2.
Therefore, the absolute value inequality for the given conditions is |x - 8| ≤ 2.