Number Line Definition Examples Inequalities Cuemath

Bonisiwe Shabane

-Oct 31, 2025, 2:44 AM

number line definition examples inequalities cuemath

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease. A visual representation of numbers on a straight line drawn either horizontally or vertically is known as a number line. Writing down numbers on a number line makes it easy for us to compare them and to perform basic arithmetic operations on them. Zero (0) is considered to be the origin of a number line.

The numbers to the left of 0 are negative numbers and the numbers to the right of 0 are all positive numbers. So, we can say that on a number line, as we move towards the right, the value of numbers increases. This means that the numbers present on the right are larger than the numbers on the left. For example, 3 comes to the right of 1, so 3 > 1. Observe the horizontal number line given below. In order to draw a number line or to plot a number on it, we use the following steps.

As we discussed above, a number line has positive and negative numbers. The section of the number line to the left side of zero forms a negative number line. While, the section on the right side of zero contains all positive numbers, and it forms a positive number line. It can be extended to infinity from both ends (right and left). The parts of a number line and some of its properties are given below. Observe the parts of a number line given below to relate to the following features of a number line.

In mathematics, inequality occurs when a non-equal comparison is made between two mathematical expressions or two numbers. In general, inequalities can be either numerical inequality or algebraic inequality or a combination of both. Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1. There are several ways to represent various kinds of linear inequalities. In this article, let us learn about linear inequalities, solving linear inequalities, graphing linear inequalities. Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.

The five symbols that are used to represent the linear inequalities are listed below: We need to note that if, p < q, then p is some number that is strictly less than q. If p ≤ q, then it means that p is some number that is either strictly less than q or is exactly equal to q. Likewise, the same applies to the remaining two inequalities > (greater than) and ≥ (greater than or equal to). Now, Let's say we have a linear inequality, 3x - 4 < 20. In this case LHS < RHS.

We can see that the expression on the left-hand side, that is, 3x - 4 is in fact lesser than the number on the right-hand side, which is 20. We can represent this inequality pictorially on a weighing scale as: High Impact Tutoring Built By Math Experts Personalized standards-aligned one-on-one math tutoring for schools and districts In order to access this I need to be confident with: Here you will learn about inequalities on a number line, including how to represent inequalities on a number line, interpret inequalities from a number line, and list integer values from an inequality.

Students will first learn about inequalities on a number line as part of expressions and equations in 6th grade. In Mathematics, equations are not always about being balanced on both sides with an 'equal to' symbol. Sometimes it can be about 'not an equal to' relationship like something is greater than the other or less than. In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. These mathematical expressions come under algebra and are called inequalities. Let us learn the rules of inequalities, and how to solve and graph them.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. Olivia is selected in the 12U Softball. How old is Olivia? You don't know the age of Olivia, because it doesn't say "equals".

But you do know her age should be less than or equal to 12, so it can be written as Olivia's Age ≤ 12. This is a practical scenario related to inequalities. The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things. Absolute value inequalities are inequalities in algebra that involve algebraic expressions with absolute value symbols and inequality symbols. In simple words, we can say that an absolute value inequality is an inequality with an absolute value symbol in it.

It can be solved using two methods of either the number line or the formulas. An absolute value inequality is a simple linear expression in one variable and has symbols such as >, <, >, <. In this article, we will learn the concept of absolute value inequalities and the methods to solve them. We will mainly focus on the linear absolute value inequalities and discuss how to graph them with the help of various solved examples for a better understanding of the concept. An absolute value inequality is an inequality that involves an absolute value algebraic expression with variables. Absolute value inequalities are algebraic expressions with absolute value functions and inequality symbols.

That is, an absolute value inequality can be one of the following forms (or) can be converted to one of the following forms: So the absolute value inequalities are of two types. They are either of lesser than or equal to or are of greater than or equal to forms. The two varieties of inequalities are as follows. In this section, we will learn to solve the absolute value inequalities. Here is the procedure for solving absolute value inequalities using the number line.

The procedure to solve the absolute value inequality is shown step-by-step along with an example for a better understanding. In this mini-lesson, we will learn about infinite sets, ordered pairs, graph linear inequalities in two variables, greater than or equal to, less than or equal to, linear inequalities in two variables and graphing... But here's an interesting bit of trivia: Did you know that Thomas Harriot was the person who introduced the concept of inequalities in his book "Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas" in 1631. When one expression is given to be greater than or less than another expression, we have an inequality. Linear inequalities are defined as expressions where two values are compared using inequality symbols. The symbols representing inequalities are:

Not equal (\(\neq\)) Less than (\(<\)) Greater than (\(>\)) Less than or equal to (\(\leq\)) Greater than or equal to (\(\geq\)) Our chosen students improved 1.19 of a grade on average - 0.45 more than those who didn't have the tutoring. In order to access this I need to be confident with: Here we will learn about inequalities on a number line including how to represent inequalities on a number line, interpret inequalities from a number line and list integer values from an inequality. There are also inequalities on a number line worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck. Inequalities on a number line allow us to visualise the values that are represented by an inequality.

Linear Inequalities are mathematical statements that show the relationship between two expressions using inequality symbols instead of an equal sign. They are similar to a linear equation, but instead of “=”, they use symbols like: Linear inequalities are formed by combining linear algebraic expressions with inequalities. A linear algebraic expression has a degree of one, meaning it involves terms of degree one. In linear inequalities, at least one quantity being compared must be a polynomial. Following are some examples of linear inequalities with their meaning:

Quadratic inequalities can be derived from quadratic equations. The word “quadratic” comes from the word “quadrature”, which means "square" in Latin. From this, we can define quadratic inequalities as second-degree inequation. Here, we first define a quadratic equation. The general form of a quadratic equation is ax2 + bx + c = 0. Further if the quadratic polynomial ax2 + bx + c is not equal to zero, then they are either ax2 + bx + c > 0, or ax2 + bx + c < 0,...

In this mini-lesson, we will learn about quadratic inequality, solving quadratic inequalities, quadratic inequalities in one variable, quadratic inequalities formula, and the graph of quadratic inequality, with the help of examples, FAQs. The quadratic inequality is a second-degree expression in x and has a greater than (>) or lesser than (<) inequality. the quadratic inequality has been derived from the quadratic equation ax2 + bx + c = 0. Let us check the definition of quadratic inequality, the standard form, and the examples of quadratic inequalities. If a quadratic polynomial in one variable is less than or greater than some number or any other polynomial (with a degree less than or equal to 2), then it is said to be... The difference between a quadratic equation and a quadratic inequality is that the quadratic equation is equal to some number while quadratic inequality is either less than or greater than some number.

Some examples of quadratic inequalities in one variable are: The standard form of quadratic inequalities in one variable is almost the same as the standard form of a quadratic equation. The only difference is that the quadratic equation has an "equal to" sign in it while a quadratic inequality has a "greater than" or "less than" sign (> or <). The standard form of quadratic inequality can be represented as: In this article, we will discuss how to solve inequalities and represent them on a number line. Video Tutorial on GCSE Maths: Inequalities on a Number Line

Number Line Definition Examples Inequalities Cuemath

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