Less Than Equal To is an inequality concept that means that the term on the left-hand side of the inequality must not be greater than the term on the right-hand side, i.e. left term must be less than or at maximum equal to the right term. The article covers the concept of "less than or equal to" in mathematics, introducing the symbol "≤" and its depiction on a number line. It includes a table of mathematical symbols, practice problems, and answers to frequently asked questions about inequalities.
Less Than Equal to Sign
The less than equal to sign is added in the image below,
What is Less Than or Equal To?
"Less than or equal to" means that one thing is not more than another or can be the same. For example, if we have 2x - 3 ≤ 9, it means that 2 times a number (x) minus 3 is not more than 9. Simplifying, if we add 3 to both sides, we get 2x ≤ 12. Then, by dividing both sides by 2, we find x ≤ 6. So, it's saying the number (x) can be 6 or less, and it's still true.
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Less Than Equal To Example
Let's say John and Peter are two friends and the age of John is less than or equal to Peter. It means John is either younger or equal to the Age of Peter. In other words, we can say that Peter is either older or minimum equal to the age of John.
Now, let's say John's age is x years and that of Peter is 'y' years then in the form of the equation involving Less Than Equal to we can write this as:
x ≤ y
where,
- x is John's Age
- y is Peter's Age
Less Than or Equal To Symbol
Symbol of "less than or equal to." is "≤"
It's used in mathematics to compare two quantities. Specifically, when you see a ≤ b, it means that a is either less than or equal to b. This symbol combines the idea of "less than" ("<") and "equal to" ("="). So, it indicates that the value on the left side of the symbol is either smaller than or the same as the value on the right side. This helps express relationships between numbers or mathematical expressions where one can be less than the other or equal to it.
Less Than or Equal To on a Number Line
The concept of "less than or equal to" on a number line is a fundamental mathematical expression utilized for comparing numerical values. In this context, it signifies that a given number is either smaller than or equal to another number. When representing this relationship on a number line, a closed circle (●) is placed on the point corresponding to the smaller or equal value. For Example, x ≤ 2 is represented as follows on the number line
Additionally, a line extends to the right from this point, encompassing all the numbers that are greater than or equal to the designated value. The inclusion of a closed circle serves to emphasize that the endpoint is part of the comparison. To illustrate, if A ≤ B, point A may be positioned at or to the left of point B on the number line, indicating that A is either less than or equal to B, with inclusivity towards the possibility that A is equal to B. This visual representation aids in comprehending the relative magnitudes of the compared values.
Symbol Notations of Inequalities
The various inequalities sign used along with their description is added below:
|
|
Greater than sign
| >
|
Less than sign
| <
|
Equal to sign
| =
|
Not equal to sign
| ≠
|
Greater less or equal to
| ≥
|
Less than or equal to
| ≤
|
Less Than Equal To and Greater Than Equal To
The comparison between Greater Than Equal To and Less Than Equal to mentioned below:
|
|
Indicates Value which is larger or minimum equal to the given value
| Indicate Value which is smaller or at maximum equal to given value
|
|
≥
|
≤
|
Age of Ram is Greater Than equal to 10 years
⇒ Age of Ram ≥ 10
| Age of Rohan is Less Than equal to 15 years
⇒ Age of Rohan ≤ 15
|
Related Reads,
Less Than Equal To - Examples
Example 1. Solve the inequality: 3x - 5 ≤ 10.
Solution:
Start by adding 5 to both sides:
3x ≤ 15
Then, divide by 3: x ≤ 5
So, the solution is x ≤ 5
Example 2. Solve the inequality: -2y + 7 ≤ 1.
Solution:
Subtract 7 from both sides: -2y ≤ -6
Divide by -2, remembering to reverse the inequality sign: y ≥ 3
The solution is y ≥ 3
Less Than Equal To - Practice Problems
Try out the following Practice Problems based on Concept of Less Than Equal To
Q1. Solve the inequality: "2y - 8 is less than or equal to 10."
Q2. If m is 6 and n is 3, determine whether "m squared minus 5" is less than or equal to "2n plus 1."
Q3. Solve for x: "3x plus 7 is less than or equal to 22."
Q4. If q is a positive number such that "4q minus 6 is less than or equal to 14," find the possible values for q.
Q5. Determine the range of values for "a" that satisfy the inequality "2a plus 5 is less than or equal to 15."
Less Than Equal To - FAQs
1. What is "Less than or Equal to"?
"Less than or equal to" denotes a relationship between two values, implying that the first value is either smaller or equal to the second.
2. How is "Less than or Equal to" represented on a number line?
On a number line, this relationship is visually depicted by placing a closed circle (●) on the number corresponding to the smaller or equal value and extending a line to the right, encompassing all numbers greater than or equal to that value.
3. What does Closed Circle Signify on Number Line?
The closed circle emphasizes the inclusion of the endpoint in the comparison. If, for example, A ≤ B, it indicates that point A is either at or to the left of point B on the number line, inclusive of the possibility that A equals B.
4. What is an Example of solving a "Less Than or Equal To" Inequality?
Consider the inequality 2x - 3 ≤ 9. If we add 3 to both sides, we get 2x ≤ 12. Then, by dividing both sides by 2, we find x ≤ 6. Therefore, the solution to the inequality is x ≤ 6.
5. How do Solve Inequalities Involving "Less Than or Equal To"?
To solve inequalities like "ax + b ≤ c," the usual approach involves manipulating the inequality through addition, subtraction, multiplication, or division to isolate the variable and determine the range of values that satisfy the inequality.
6. What is Symbol of Less Than Equal To and Greater Than Equal To?
Symbol of Less Than Equal to is ≤ while the symbol of greater than equal to is ≥.
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