What does ≥ mean in an inequality?
The inequalities contain four operators, which are: less than {eq}<, {/eq} less than or equal to {eq}<=, {/eq} greater than {eq}>, {/eq} and greater than or equal to {eq}>=. {/eq} Show
The greater than or equal to means the value is greater than the given value and the given value is included. It is also denoted by the term at least. The less than or equal to means the value is lesser than the given value and the given value is also included. It is also denoted by the term no more than. In math, an inequality shows the relationship between two values in an algebraic expression that are not equal. Inequality signs can indicate that one variable of the two sides of the inequality is greater than, greater than or equal to, less than, or less than or equal to another value. Whether a sign is greater than or less than depends on the direction of the inequality sign. If the open part of the sign is turned towards the left side, >, the value on the left side of the sign is greater than the right. If it's turned towards the right side, <, the value on the left is less than the value on the right. Some inequality symbols will have a line underneath them: ≥ and ≤. This means that the two sides of an inequality expression could potentially be equal. However, not enough is known to prove this. As you can see in the mathematical expression above, x, is greater than or equal to 7. Because x can be many values, saying it’s equal to 7 wouldn't be a true statement. That's why we must use .Inequalities on a Number LineWhenever a linear inequality has a variable and a real number, you can express it on a number line. Here's how to use number lines to show x is greater than positive number 3 and less than or equal to negative number -1: Any number line showing a linear inequality must have an open circle for < and > and a closed circle for ≤ and ≥. Using Interval NotationWhen we know an inequality is between two numbers, you can write it in interval notation. Interval notation expresses the location range of an inequality by using brackets for ≥ and ≤ signs and parentheses for < and > signs. Here's how you would show that y is less than or equal to -4 and 2 is greater than y: As you can see, we use an open circle to show that y is less than 2 and a closed circle to show that y is equal to or greater than -4. In linear notation, this is written as: Linear Notation: [-4, 2) Answering ‘What Is an Inequality?’Understanding the concept of inequalities allows us to better understand linear equations and the number line. When we know that a variable, like x or y, is within a specific range of values, we can represent it by shading that range of numbers on the number line. On this line, we use an open circle for greater than or less than values and a closed circle for equal to or less than and equal to or greater than values. If we know the inequality is between two numbers, we can use brackets and parentheses to show the possible range of the inequality’s values in linear notation. Learn on the go with worksheets to print out – combined with the accompanying videos, these worksheets create a complete learning unit. 24-hour help provided by teachers who are always there to assist when you need it. 89% of students improve their grades with sofatutor Try 30 days for free End free trial at any time online Rating Ø 5.0 / 1 ratings You must be logged in to be able to give a rating. Wow, thank you! The authors Eugene Lee Basics on the topic Inequality Symbols: <, >, ≤, ≥Inequality symbols are a shorthand notation used to compare different quantities. There are four inequality symbols “greater than”, “less than”, “greater than or equal to”, and “less than or equal to”. So, for instance, the sentence “5 is greater than 2” can be written as 5>2. A good way to remember which number is greater is to think of each symbol like a mouth; the mouth will always eat the larger of the two numbers being compared. Learn about inequality symbols by helping Christopher the vampire pack the maximum number of supplies he needed for his trip to California. Common Core Reference: CCSS.MATH.CONTENT.6.EE.B.8 Transcript Inequality Symbols: <, >, ≤, ≥Christopher the Vampire is a foodie and he needs a fresh, new story for his blog: The Vegetarian Vampire. He’s working on a new piece, so he wants to go to a place where his favorite fruit grows: the blood orange. He read on Vampedia that blood oranges grow in California, which is perfect because he’s always wanted to visit the underground gardens there. To help him pack, he uses his knowledge of inequality symbols. And he has all his supplies laid out in his bed? Capes, check. Hair gel, check. Blood orange juice, check. But how much of this stuff is he allowed to carry with him on the plane? Let's take a look at the number line. Use of inequalitiesChristopher the Vampire’s trip will last fewer than 15 days. For inequailties with 'less than', we use this sign <. Furthermore, for this trip, Chris can't take more than 1000ml of blood orange juice on the plane. For inequalities like 'less than or equal to' we use this symbol: ≤. Our foodie vampire also needs to pack more than 1 bottle of hair gel, since he ran out during his last vacation. Let's draw this on the number line. For inequalities with 'more than', we use the 'greater than' symbol. He also needs to pack at least 16 capes, one for each day and two, just in case. For inequalities with 'at least', we use the 'greater than or equal to' symbol. Inequalities summary - Imagine a mouthLet's take another look at the different inequality symbols. A good way to remember which number is greater, is to think of each sign like a mouth. The mouth will always eat the larger of the two numbers being compared. For example let's compare 2 and 4. Since 2 is less than 4, the mouth will eat the 4. If the mouth opens to the right, it's read: 'a' is less than 'b'. However, if the mouth opens to the left, it's read: 'a' is greater than 'b'. As we saw earlier, the greater than and less than symbols can also be combined with the equal sign. When we say 'as many as' or 'no more than', we mean 'less than or equal to' which means that a could be less than b or equal to b. But, when we say 'at least', we mean 'greater than or equal to'. Here a could be greater than b or equal to b. Let’s see how Christopher the Vampire is enjoying his vacation. OH NO! No more blood oranges?!? This might make his vacation a bit tougher... READ MOREInequality Symbols: <, >, ≤, ≥ exerciseWould you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Inequality Symbols: <, >, ≤, ≥.
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