Subjects

Maths

Systems of equations

Solving systems of equations with substitution

Systems of equations with substitution: -3x-4y=-2 & y=2x-5

Easy Ways to Solve Quadratic Equations and Fractions!

Name: Knowunity
Brand: Knowunity

View

Easy Ways to Solve Quadratic Equations and Fractions!

Olaoluwa Erinfolami

@olaoluwaerinfolami_pbuj

6 Followers

This guide provides a comprehensive overview of solving equations and inequalities, covering various types of problems and solution methods. It is designed to help students understand and practice these fundamental mathematical concepts.

Key topics include:

Solving linear and quadratic equations
Handling equations with fractions
Understanding and solving inequalities
Working with negative coefficients in inequalities
Solving complex inequalities involving fractions

The guide offers numerous examples with step-by-step solutions, as well as practice exercises for students to apply their knowledge.

7/28/2022

412

Equations
and
Inequalities Solving Equations
Example 1.
Solve
5x+ 3 = 38 Example 2.
Solve 2x = 6x + 14 Example 3.
Solve
7x - 8 = 2x + 18 Exa

View

Solving Linear Inequalities

This page demonstrates solving a simple linear inequality: 3x > 2x + 6.

Example: To solve 3x > 2x + 6, subtract 2x from both sides: x > 6. The solution is x > 6, which can be represented on a number line.

This example introduces the basic steps for solving linear inequalities, emphasizing the importance of isolating the variable.

View

Additional Resources for Inequalities with Fractions

This page provides information about additional practice resources specifically for inequalities involving fractions.

Highlight: The resources mentioned include "Inequalities with Fractions 1" and "Inequalities with Fractions 2", offering targeted practice for this challenging topic.

These resources are crucial for students looking to master the complex skills involved in solving inequalities with fractions, providing opportunities for further practice and reinforcement of the concepts covered in the guide.

View

Solving Equations with Fractions and Variables

This page demonstrates solving an equation with fractions and variables in different positions: x/2 - 1/3 = 2/(x+5).

Example: Multiply all terms by 6(x+5) to eliminate fractions: 3x(x+5) - 2(x+5) = 12. Expand and simplify to get a quadratic equation, then solve using appropriate methods.

This example illustrates how to solve equations with fractions and variables in both numerators and denominators, introducing more advanced problem-solving techniques.

View

Practice Problems: Equations with Fractions

This page provides additional practice problems focusing on equations with fractions.

Highlight: These problems range from simple fractional equations to more complex ones involving variables in denominators and mixed fractions, allowing students to apply the techniques learned in previous sections.

The practice problems are essential for reinforcing the concepts of solving equations with fractions, giving students the opportunity to develop their skills further.

View

Solving Equations with Variables on Both Sides

This page presents a more complex equation: 2x = 6x + 14.

Example: To solve 2x = 6x + 14, subtract 2x from both sides to get 0 = 4x + 14. Then subtract 14 from both sides and divide by 4 to find x = -3.5.

This example demonstrates how to handle equations with variables on both sides, teaching students to group like terms before solving.

View

Solving Equations with Parentheses

This page demonstrates solving an equation with parentheses: 3(x + 7) = 4(x - 3) + 10.

Example: First, distribute the coefficients: 3x + 21 = 4x - 12 + 10. Simplify the right side: 3x + 21 = 4x - 2. Subtract 3x from both sides: 21 = x - 2. Add 2 to both sides to get x = 23.

The example teaches students how to handle equations with parentheses by distributing coefficients before solving.

View

Solving Linear Equations

This page demonstrates how to solve a simple linear equation: 5x + 3 = 38.

Example: To solve 5x + 3 = 38, subtract 3 from both sides, then divide by 5 to isolate x. The solution is x = 7.

The example illustrates the basic steps for solving linear equations, which involve isolating the variable on one side of the equation.

View

Solving Word Problems with Equations

This page presents a word problem involving areas of rectangles, teaching students how to translate real-world scenarios into equations.

Example: Two rectangles with dimensions x + 8 by x, and x + 3 by x + 4, have the same area. Set up the equation: x(x + 8) = (x + 3)(x + 4). Solve to find x = 1/2.

The example shows how to apply equation-solving skills to practical problems, enhancing students' problem-solving abilities.

View

Introduction to Equations with Fractions

This page introduces the concept of solving equations with fractions, using the example: 1/3x + 1/4 = 6/4.

Example: To solve 1/3x + 1/4 = 6/4, first multiply all terms by 12 (the LCM of 3 and 4) to eliminate fractions: 4x + 3 = 18. Then subtract 3 from both sides and divide by 4 to get x = 15/4.

This example demonstrates how to solve equations with fractions step by step, introducing students to techniques for handling fractional coefficients and constants.

View

Solving Complex Fractional Equations

This page presents a complex equation involving fractions and exponents: 3/4 + 5²/(x-1)² = 1/3x.

Example: Multiply all terms by 12x(x-1)² to eliminate fractions: 9x(x-1)² + 300x = 4(x-1)². Expand and simplify to get a cubic equation, then solve using appropriate methods.

This example demonstrates advanced techniques for solving equations with fractions, incorporating exponents and complex algebraic manipulations.

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.

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

Subjects

Maths

Systems of equations

Solving systems of equations with substitution

Systems of equations with substitution: -3x-4y=-2 & y=2x-5

Easy Ways to Solve Quadratic Equations and Fractions!

Olaoluwa Erinfolami

@olaoluwaerinfolami_pbuj

6 Followers

Key topics include:

Solving linear and quadratic equations
Handling equations with fractions
Understanding and solving inequalities
Working with negative coefficients in inequalities
Solving complex inequalities involving fractions

The guide offers numerous examples with step-by-step solutions, as well as practice exercises for students to apply their knowledge.

7/28/2022

412

Maths

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Solving Linear Inequalities

This page demonstrates solving a simple linear inequality: 3x > 2x + 6.

Example: To solve 3x > 2x + 6, subtract 2x from both sides: x > 6. The solution is x > 6, which can be represented on a number line.

This example introduces the basic steps for solving linear inequalities, emphasizing the importance of isolating the variable.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Additional Resources for Inequalities with Fractions

This page provides information about additional practice resources specifically for inequalities involving fractions.

Highlight: The resources mentioned include "Inequalities with Fractions 1" and "Inequalities with Fractions 2", offering targeted practice for this challenging topic.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Solving Equations with Fractions and Variables

This page demonstrates solving an equation with fractions and variables in different positions: x/2 - 1/3 = 2/(x+5).

Example: Multiply all terms by 6(x+5) to eliminate fractions: 3x(x+5) - 2(x+5) = 12. Expand and simplify to get a quadratic equation, then solve using appropriate methods.

This example illustrates how to solve equations with fractions and variables in both numerators and denominators, introducing more advanced problem-solving techniques.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Practice Problems: Equations with Fractions

This page provides additional practice problems focusing on equations with fractions.

Highlight: These problems range from simple fractional equations to more complex ones involving variables in denominators and mixed fractions, allowing students to apply the techniques learned in previous sections.

The practice problems are essential for reinforcing the concepts of solving equations with fractions, giving students the opportunity to develop their skills further.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Solving Equations with Variables on Both Sides

This page presents a more complex equation: 2x = 6x + 14.

Example: To solve 2x = 6x + 14, subtract 2x from both sides to get 0 = 4x + 14. Then subtract 14 from both sides and divide by 4 to find x = -3.5.

This example demonstrates how to handle equations with variables on both sides, teaching students to group like terms before solving.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Solving Equations with Parentheses

This page demonstrates solving an equation with parentheses: 3(x + 7) = 4(x - 3) + 10.

Example: First, distribute the coefficients: 3x + 21 = 4x - 12 + 10. Simplify the right side: 3x + 21 = 4x - 2. Subtract 3x from both sides: 21 = x - 2. Add 2 to both sides to get x = 23.

The example teaches students how to handle equations with parentheses by distributing coefficients before solving.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Solving Linear Equations

This page demonstrates how to solve a simple linear equation: 5x + 3 = 38.

Example: To solve 5x + 3 = 38, subtract 3 from both sides, then divide by 5 to isolate x. The solution is x = 7.

The example illustrates the basic steps for solving linear equations, which involve isolating the variable on one side of the equation.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Solving Word Problems with Equations

This page presents a word problem involving areas of rectangles, teaching students how to translate real-world scenarios into equations.

Example: Two rectangles with dimensions x + 8 by x, and x + 3 by x + 4, have the same area. Set up the equation: x(x + 8) = (x + 3)(x + 4). Solve to find x = 1/2.

The example shows how to apply equation-solving skills to practical problems, enhancing students' problem-solving abilities.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Introduction to Equations with Fractions

This page introduces the concept of solving equations with fractions, using the example: 1/3x + 1/4 = 6/4.

Example: To solve 1/3x + 1/4 = 6/4, first multiply all terms by 12 (the LCM of 3 and 4) to eliminate fractions: 4x + 3 = 18. Then subtract 3 from both sides and divide by 4 to get x = 15/4.

This example demonstrates how to solve equations with fractions step by step, introducing students to techniques for handling fractional coefficients and constants.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Solving Complex Fractional Equations

This page presents a complex equation involving fractions and exponents: 3/4 + 5²/(x-1)² = 1/3x.

Example: Multiply all terms by 12x(x-1)² to eliminate fractions: 9x(x-1)² + 300x = 4(x-1)². Expand and simplify to get a cubic equation, then solve using appropriate methods.

This example demonstrates advanced techniques for solving equations with fractions, incorporating exponents and complex algebraic manipulations.

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.

Download in

Google Play

Download in

App Store

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

Easy Ways to Solve Quadratic Equations and Fractions!

Solving Linear Inequalities

Additional Resources for Inequalities with Fractions

Solving Equations with Fractions and Variables

Practice Problems: Equations with Fractions

Solving Equations with Variables on Both Sides

Solving Equations with Parentheses

Solving Linear Equations

Solving Word Problems with Equations

Introduction to Equations with Fractions

Solving Complex Fractional Equations

Similar Content

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.

4.9+

13 M

#1

950 K+

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

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

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

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

Easy Ways to Solve Quadratic Equations and Fractions!

Sign up to see the content. It's free!

Solving Linear Inequalities

Sign up to see the content. It's free!

Additional Resources for Inequalities with Fractions

Sign up to see the content. It's free!

Solving Equations with Fractions and Variables

Sign up to see the content. It's free!

Practice Problems: Equations with Fractions

Sign up to see the content. It's free!

Solving Equations with Variables on Both Sides

Sign up to see the content. It's free!

Solving Equations with Parentheses

Sign up to see the content. It's free!

Solving Linear Equations

Sign up to see the content. It's free!

Solving Word Problems with Equations

Sign up to see the content. It's free!

Introduction to Equations with Fractions

Sign up to see the content. It's free!

Solving Complex Fractional Equations

Similar Content

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.

4.9+

13 M

#1

950 K+

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

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

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

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