The absolute value of the difference between the stock trading price and $70.85 cannot be greater than $0.75.
{m | 70.10≤ m≤ 71.60}
Practice makes perfect
To calculate the difference between the purchase price of Jerome's stock, $70.85, and one of the price fluctuations, we would subtract the original price from the current price.
Current price-Original price=Price fluctuation
If we call the current price m and substitute the given original price, we can specify our expression.
m-70.85=price fluctuation
We are told that when the stock drops below Jerome's original purchasing price, it drops no more than $0.75. Furthermore, when the stock rises it rises no more than $0.75. Therefore, m-70.85 is greater than or equal to - 0.75 and less than or equal to 0.75. We can express this inequality in two different ways.
Absolute Value:& |m-70.85|≤ 0.75
Compound:& - 0.75 ≤ m-70.85 ≤ 0.75
Note that there is a third way to write this and type of compound inequality.
- 0.75≤ m-70.85 and m-70.85 ≤ 0.75
Let's isolate m in both of these cases before recombining them to form the final solution set.
Case 1
Let's look at the case for the price dropping, - 0.75≤ m-70.85.
This inequality is true when m is less than or equal to 71.60.
Range of Stock Prices
The solution to this type of compound inequality is the intersection of the solution sets.
First Solution Set:& 70.10 ≤ m
Second Solution Set:& m ≤ 71.60
Intersecting Solution Set:& 70.10 ≤ m ≤ 71.60
The value of Jerome's stock lies in the interval $70.10≤ m≤ $71.60.
We can then write the solution set in set-builder notation, as {m | 70.10≤ m≤ 71.60}.
