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How to Graph Linear Inequalities Step by Step - Easy for Kids!

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How to Graph Linear Inequalities Step by Step - Easy for Kids!

Linear inequalities are mathematical expressions that involve variables and inequality symbols. They are used to represent relationships between quantities that are not exactly equal. This guide explains how to solve and graph linear inequalities, providing step-by-step instructions and examples.

Solving linear inequalities involves finding values that satisfy the inequality.
Graphing linear inequalities requires drawing a line and shading the appropriate region.
• Solutions to linear inequalities are represented as ordered pairs or regions on a coordinate plane.
• Understanding inequality symbols and their graphical representations is crucial for solving these problems.

1/30/2023

791

solving linear inequalities
A linear inequality is similar to a linear equation, but
the equal sign is replaced with an inequality symbol. A

Solving and Graphing Linear Inequalities

Linear inequalities are mathematical expressions similar to linear equations, but they use inequality symbols instead of an equal sign. This page covers how to identify solutions and graph linear inequalities.

Identifying Solutions

A solution to a linear inequality is any ordered pair that makes the inequality true. To determine if an ordered pair is a solution, substitute the values into the inequality and check if it holds true.

Example: For the inequality y < x - 1, we can check if (7, 3) is a solution: 3 < 7 - 1 3 < 6 This is true, so (7, 3) is a solution.

Example: For the inequality y > 3x + 2, we can check if (4, 5) is a solution: 5 > 3(4) + 2 5 > 14 This is false, so (4, 5) is not a solution.

Graphing Inequalities

When graphing linear inequalities, the type of line and shading used depends on the inequality symbol:

Highlight:

  • For y ≤ or y ≥, use a solid line.
  • For y < or y >, use a dashed line.
  • For > or ≥, shade above the line.
  • For < or ≤, shade below the line.

Vocabulary:

  • Solid line: A continuous, unbroken line used for inequalities that include the boundary (≤ or ≥).
  • Dashed line: A line made up of short, disconnected segments used for strict inequalities (< or >).

Understanding these rules is crucial for graphing linear inequalities step by step. When using a graphing linear inequalities calculator, it's important to input the inequality correctly to ensure accurate shading and line type.

Definition: A system of linear inequalities consists of two or more linear inequalities that must be satisfied simultaneously. The solution is the region where all inequalities are true.

Practicing with a graphing linear inequalities worksheet can help reinforce these concepts and improve your skills in solving linear inequalities with two variables. Remember, the solution of an inequality is not just a single point, but an entire region on the coordinate plane that satisfies the given conditions.

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Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

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Knowunity is the # 1 ranked education app in five European countries

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In Education App Charts in 12 Countries

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I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

How to Graph Linear Inequalities Step by Step - Easy for Kids!

Linear inequalities are mathematical expressions that involve variables and inequality symbols. They are used to represent relationships between quantities that are not exactly equal. This guide explains how to solve and graph linear inequalities, providing step-by-step instructions and examples.

Solving linear inequalities involves finding values that satisfy the inequality.
Graphing linear inequalities requires drawing a line and shading the appropriate region.
• Solutions to linear inequalities are represented as ordered pairs or regions on a coordinate plane.
• Understanding inequality symbols and their graphical representations is crucial for solving these problems.

1/30/2023

791

 

Algebra 1

348

solving linear inequalities
A linear inequality is similar to a linear equation, but
the equal sign is replaced with an inequality symbol. A

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Solving and Graphing Linear Inequalities

Linear inequalities are mathematical expressions similar to linear equations, but they use inequality symbols instead of an equal sign. This page covers how to identify solutions and graph linear inequalities.

Identifying Solutions

A solution to a linear inequality is any ordered pair that makes the inequality true. To determine if an ordered pair is a solution, substitute the values into the inequality and check if it holds true.

Example: For the inequality y < x - 1, we can check if (7, 3) is a solution: 3 < 7 - 1 3 < 6 This is true, so (7, 3) is a solution.

Example: For the inequality y > 3x + 2, we can check if (4, 5) is a solution: 5 > 3(4) + 2 5 > 14 This is false, so (4, 5) is not a solution.

Graphing Inequalities

When graphing linear inequalities, the type of line and shading used depends on the inequality symbol:

Highlight:

  • For y ≤ or y ≥, use a solid line.
  • For y < or y >, use a dashed line.
  • For > or ≥, shade above the line.
  • For < or ≤, shade below the line.

Vocabulary:

  • Solid line: A continuous, unbroken line used for inequalities that include the boundary (≤ or ≥).
  • Dashed line: A line made up of short, disconnected segments used for strict inequalities (< or >).

Understanding these rules is crucial for graphing linear inequalities step by step. When using a graphing linear inequalities calculator, it's important to input the inequality correctly to ensure accurate shading and line type.

Definition: A system of linear inequalities consists of two or more linear inequalities that must be satisfied simultaneously. The solution is the region where all inequalities are true.

Practicing with a graphing linear inequalities worksheet can help reinforce these concepts and improve your skills in solving linear inequalities with two variables. Remember, the solution of an inequality is not just a single point, but an entire region on the coordinate plane that satisfies the given conditions.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying