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The inequality \( x \leq 5 \) means that x can be any number less than or equal to 5.
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The inequality x ≤ 5 means that x can be any real number that is less than or equal to 5.
• In interval notation, the solution set is: (-∞, 5].
• If you were to graph this on a number line, you would draw a filled (closed) circle at 5 to show that 5 is included, and then shade the line to the left of 5, representing all values less than 5.
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This inequality tells us that \( x \) can take any value that is less than or equal to 5. Imagine you're at a party where the "maximum guest limit" is set to 5 people. You could have 0, 1, 2, 3, 4, or 5 guests—but no more! When solving inequalities like this, remember to consider endpoints carefully, especially if you're graphing on a number line. A closed dot at 5 signifies that 5 is included, but don’t forget that as we move left (toward smaller values), all those options are open!
