If the normal pressure of the tank is 2500 and is capable of varying by ± 500, what is the minimum pressure? What is the maximum?
{x | 2000< x< 3000}
Practice makes perfect
To calculate the difference between the normal pressure and actual pressure, we can subtract the normal pressure from the actual pressure.
actual pressure-normal pressure=difference
If we call the actual pressure x and substitute the given normal pressure we can specify our expression.
x-2500=differenceWe are told that the pressure difference should be within 500 psi. Therefore, x-2500 should be greater than - 500 andless than 500. We can express this inequality in two different ways.
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Absolute Value:& | x-2500| < 500
Compound:& - 500 < x-2500 < 500
Note that there is a third way to write this and type of compound inequality.
- 500 < x-2500 and x-2500 < 500
Let's isolate x in both of these cases before recombining them to form the final solution set.
Case 1
We can isolate x in the inequality - 500 < x-2500.
The solution to this type of compound inequality is the intersection of the solution sets.
First Solution Set: 2000 < x&
Second Solution Set: x& < 3000
Intersecting Solution Set: 2000< x& < 3000
The range of optimum pressures is 2000 < x < 3000. We can write this solution set in set-builder notation as follows.
{x | 2000< x< 3000}
