For a certain hydraulic press to operate safely, the pressure , measured in pounds per square inch (psi), must satisfy
Which of the following could be the pressure reading when the machine is in safe operating condition?
For inequality questions with specific answer choices, first translate the inequality into plain language (for example, “greater than 40 and at most 55”). Then quickly test each option against both parts of the inequality, paying close attention to whether the endpoints are included (, ) or excluded (, ). Eliminate any choice that fails even one part of the condition, and choose the one that satisfies all parts.
Hints
Focus on the inequality signs
Look closely at the symbols and in . One of them allows equality, and the other does not. Which is which?
Think about the boundary values
Is a pressure of exactly 40 psi allowed by ? Is a pressure of exactly 55 psi allowed by ?
Test each choice against the rule
For each answer choice, ask: Is it greater than 40? Is it less than or equal to 55? Only a choice that passes both tests is acceptable.
Desmos Guide
Check each option as a logical statement
In Desmos, you can type each condition directly to see if it is true or false, for example:
- Type
40 < 39.9 <= 55 - Type
40 < 40 <= 55 - Type
40 < 55 <= 55 - Type
40 < 55.2 <= 55
Look at which line evaluates to true; that pressure reading satisfies the safe operating condition.
Step-by-step Explanation
Understand the inequality symbols
The safe operating condition is given by
This means:
- must be greater than 40 (not equal to 40).
- must be less than or equal to 55 (it can equal 55, but not be larger).
Translate the condition into words
Restate the inequality as a sentence: the pressure must be more than 40 psi and at most 55 psi.
Any value that is 40 or less is too low, and any value greater than 55 is too high.
Test each answer choice against the condition
Check each option:
- 39.9 psi is less than 40, so it fails .
- 40 psi is equal to 40, but the condition requires to be greater than 40, so it fails.
- 55 psi is equal to 55, which is allowed because of the part.
- 55.2 psi is greater than 55, so it fails .
Choose the value that satisfies both inequalities
Only one option is more than 40 and no more than 55. That option is 55 psi, so this is the pressure that could be the reading when the machine is in safe operating condition.