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Less than or Equal to: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Less than or Equal toLess than or Equal to: Definition and ExampleTable of ContentsDefinition of Less-Than-Or-Equal-To Symbol in Mathematics

The "less than or equal to" symbol (≤\leq≤) is an inequality operator used in mathematics when comparing quantities that are not equal in value but are comparable in nature. While equations define equality between mathematical elements using the "equal to (===)" symbol, inequalities use symbols like "greater than (>>>)" and "less than ()" to express relationships between unequal quantities. The "less than or equal to" symbol specifically indicates that one quantity is either less than or exactly equal to another quantity. This provides a mathematical expression for phrases such as "at most," "not more than," "maximum," and "not exceeding."

Mathematics uses several comparison symbols to establish relationships between quantities. The basic inequality symbols include "less than" () which indicates one quantity is smaller than another, and "greater than" (>>>) which shows one quantity exceeds another. The extended symbols "less than or equal to" (≤\leq≤) and "greater than or equal to" (≥\geq≥) add equality as a possibility to these comparisons. When representing these inequalities on a number line, a closed circle (filled dot) at a point indicates that value is included in the solution set, while an open circle (unfilled dot) shows that specific value is excluded.

Examples of Less-Than-Or-Equal-To Inequality Example 1: Identifying Values That Are Less Than or Equal to 55 Problem:

Select the numbers that are less than or equal to 555555 from the given set of numbers: 585858, 000, 555555, 949494, 585858, 555, 505050, 454545, 545454, 595959, 565656, 535353

Step-by-step solution: First, understand that "less than or equal to 555555" means we're looking for any number that is either smaller than 555555 or exactly 555555. Next, go through each number in the set and compare it with 555555: Is 58≤5558 ≤ 5558≤55? No, 585858 is greater than 555555 Is 0≤550 ≤ 550≤55? Yes, 000 is less than 555555 Is 55≤5555 ≤ 5555≤55? Yes, 555555 equals 555555 Is 94≤5594 ≤ 5594≤55? No, 949494 is greater than 555555 Continue this comparison for each number... Finally, gather all numbers that satisfy the condition. The numbers that are less than or equal to 555555 are: 000, 555555, 555, 505050, 454545, 545454, 535353. Example 2: Applying "Not More Than" in a Real-Life Scenario Problem:

A shop has watermelons weighing 5.35.35.3 kg, 7.67.67.6 kg, 4.54.54.5 kg, 777 kg, 666 kg and 6.16.16.1 kg. If Diana wants to buy a watermelon weighing not more than 666 kg, what are her possibilities?

Step-by-step solution: First, recognize that "not more than 666 kg" translates mathematically to "less than or equal to 666 kg" (≤6\leq 6≤6 kg). Next, examine each watermelon weight and determine if it satisfies our condition: 5.35.35.3 kg: Is 5.3≤65.3 ≤ 65.3≤6? Yes, 5.35.35.3 is less than 666 7.67.67.6 kg: Is 7.6≤67.6 ≤ 67.6≤6? No, 7.67.67.6 is greater than 666 4.54.54.5 kg: Is 4.5≤64.5 ≤ 64.5≤6? Yes, 4.54.54.5 is less than 666 777 kg: Is 7≤67 ≤ 67≤6? No, 777 is greater than 666 666 kg: Is 6≤66 ≤ 66≤6? Yes, 666 equals 666 6.16.16.1 kg: Is 6.1≤66.1 ≤ 66.1≤6? No, 6.16.16.1 is greater than 666 Therefore, Diana can choose from the watermelons weighing 5.35.35.3 kg, 4.54.54.5 kg, and 666 kg as these weights are less than or equal to 666 kg. Example 3: Graphing an Inequality on a Number Line Problem:

Graph x≤6x \leq 6x≤6 on the number line.

Step-by-step solution: First, understand that x≤6x \leq 6x≤6 means all values of x that are either less than 666 or equal to 666. Next, locate the number 666 on the number line. Since we're including the value 666 itself (because of the "equal to" part of our inequality), we mark this point with a filled circle. Then, since we need all values less than 666 as well, we draw an arrow extending from the point 666 to the left, indicating that all numbers to the left of 666 are part of our solution. Finally, our graph shows a filled circle at 666 with an arrow extending infinitely to the left, representing all real numbers less than or equal to 666. Comments(5)NNatureExplorerSeptember 16, 2025I’ve used this page to help my kids understand the ≤ symbol, and the examples made it so easy for them! The number line visual was a great touch for hands-on learning.

MCMs. CarterSeptember 10, 2025I’ve used the 'less than or equal to' definition page to help my kids with their math homework. The examples are super clear, and the number line visuals made it so much easier for them to understand!

MMomOf3AdventurersAugust 27, 2025This explanation of 'less than or equal to' was super helpful for my kid! The examples made it easy for them to grasp the concept, and the number line visuals were a great touch. Thanks!

NNatureLover75August 20, 2025I’ve used this page to explain 'less than or equal to' to my students, and the examples made it so clear! The number line visuals were especially helpful for my visual learners. Thanks for making math easier to teach!

MMathMom25July 30, 2025I’ve been using this page to help my 7th grader with inequality problems. The number line examples really made it click for him—it’s such a clear way to explain!

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