Inequalities can be represented on a number line. **Open circles are used for numbers less than or greater than (< or >).** **Closed circles are used for numbers less than or equal to and greater than or equal to (≤ or ≥)**.

Contents

- What does the open circle mean in linear inequalities?
- What do open and closed circles mean on a graph?
- What does a closed dot in an inequality mean?
- What do open circles mean on a graph?
- Is a closed dot a bracket?
- When graphing an inequality a closed circle means that the number is included?
- What does an open circle mean in math equation?
- Is an open circle undefined?
- What does the filled in circle mean in inequalities?
- What does an open dot mean in functions?
- How do you tell if an equation is open or closed?
- Is an open circle a bracket?
- Is open or closed circle?
- Is a closed or open bracket?
- When graphing inequality we use a closed point or shaded circle If the symbol is greater than or less than?

When graphing a linear inequality on a number line, use an open circle for **“less than” or “greater than”** and a closed circle for “less than or equal to” or “greater than” . than or equal”. Draw the solution set of: -3 < x < 4. The solution set to this problem consists of all values satisfying both -3 < x and x < 4.

Explanation: **An open circle indicates “less than” or “greater than”, while a closed circle indicates “greater than or equal to” or “less than or equal to”**.

Representing inequalities in one variable

When the inequality is “strict” ( < or > ), we use an open point to indicate that the endpoint of the ray is not part of the solution. For the other types of inequalities ( ≤ and ≥ ), we use a closed period to indicate that **the endpoint is part of the solution**.

Functions and Charts

Interval notation uses a bracket for an open endpoint and **a square bracket** for a closed endpoint. In a diagram, a filled dot is used for a closed endpoint and an empty dot for an open endpoint.

When graphing inequalities, a closed circle indicates that the number is **in the solution set**. When graphing inequalities, an open circle indicates that the number is not in the solution set. You have just studied 4 semesters!

icon. The composition symbol is a small circle: (g º f)(x) It’s not a filled dot: (g f)(x), because that means **multiply**.

**The open circle means that the function is undefined at that particular x-value**. However, limits don’t care what is actually going on with the value.

A filled circle is used for **less than or equal to**” and for “greater than or equal to”. An open circle is used for “less than” and for “greater than”.

**The circle ∘ is the symbol for composing functions**. In general, if you have two functions g:X→Y and f:Y→Z, then f∘g is a function from X to Z.

- A mathematical proposition makes a statement about two expressions.
- A closed proposition is a mathematical proposition that is known to be either true or false.
- An open theorem in math means it uses variables and doesn’t know if the math theorem is true or false.

Intervals are either open or closed or both. **Open intervals use parentheses ( ) and refer to intervals that do not contain endpoints**. Closed intervals use square or square brackets [ ] and refer to intervals containing the endpoints.

Open and closed circles. **If an inequality has an open circle, then it is less than ( < ) or greater than ( > ) in the inequality**. If it has a closed circle, then it has less than or equal to (≤) or greater than or equal to (≥) in the inequality.

A bracket, sometimes called a square bracket, is a punctuation mark that comes in pairs. There are two types of brackets: the open bracket [ and the closed bracket ] . **The open bracket has an open end to the right and the closed bracket has an open end to the left**.

A closed or shaded circle is used to represent the inequalities **greater than or equal to (≥) or less than or equal to (≤)**. The endpoint is part of the solution. An open circle is used for greater than (>) or less than (<). The endpoint is not part of the solution.

- https://mathbitsnotebook.com/Algebra1/Inequalities/IQRefresh.html
- https://www.varsitytutors.com/algebra_1-help/how-to-graph-an-inequality-with-a-number-line
- https://www.varsitytutors.com/hotmath/hotmath_help/topics/inequalities
- https://www.youtube.com/watch?v=RD4G0zXFolg
- https://web.nmsu.edu/~kberver/Unit1/Unit18.html
- https://quizlet.com/456442179/inequalities-flash-cards/
- https://www.mathsisfun.com/sets/functions-composition.html
- https://www.shmoop.com/study-guides/math/precalculus-limits/limits-and-graphs
- https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-equations-and-inequalities/cc-6th-inequalities/v/plotting-inequalities-on-a-number-line
- https://math.stackexchange.com/questions/1057050/what-does-a-mini-circle-between-f-and-hx-mean
- https://study.com/academy/lesson/open-sentence-in-math-definition-example.html
- https://flexbooks.ck12.org/cbook/ck-12-college-precalculus/section/2.2/primary/lesson/domain-and-range-c-precalc/
- http://pangea.selu.edu/~sgoodly/etec644/circle.html
- https://www.computerhope.com/jargon/b/bracket.htm
- https://courses.lumenlearning.com/waymakercollegealgebracorequisite/chapter/temp-4-review/

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