Solved Linear Equation Examples

Are you diving into the world of mathematics and finding yourself puzzled by linear equations? Don't worry; you're not alone! Understanding linear equations is crucial for building a strong foundation in algebra. In this article, we'll explore various examples of linear equations solved step by step. By the end, you'll feel more confident tackling these problems on your own.

What are linear equations?

Linear equations are algebraic expressions that represent a straight line when graphed on a coordinate plane. They typically take the form of:

Ax + B = C

Where:

• A is the coefficient of the variable x.
• B is a constant.
• C is another constant.

The main characteristic of these equations is that the highest exponent of the variable is one, making them linear in nature.

Importance of solving linear equations

Solving linear equations is a fundamental skill in mathematics with real-world applications. Here are some reasons why mastering this topic is essential:

• Foundation for Algebra: Linear equations serve as the building blocks for more complex algebraic concepts.
• Real-World Problem Solving: Many situations can be modeled using linear equations, from financial forecasts to scientific data analysis.
• Critical Thinking: The process of solving these equations enhances logical reasoning and problem-solving skills.

Examples of linear equations solved

Now, let’s dive into some practical examples. We will start with simpler equations and progress to more complex ones. Try solving them on your own before checking the solutions!

Example 1

Equation: 20 – 7x = 6x – 6

Solution Steps:

1. Rearranging the equation:

-7x - 6x = -6 - 20

2. Combine like terms:

-13x = -26

3. Divide both sides by -13:

x = 2

Example 2

Equation: 7x + 2 = 10x + 5

Solution Steps:

1. Rearranging the equation:

7x - 10x = 5 - 2

2. Combine like terms:

-3x = 3

3. Divide both sides by -3:

x = -1

Example 3

Equation: 6x - 5 = 8x + 2

Solution Steps:

1. Rearranging the equation:

6x - 8x = 2 + 5

2. Combine like terms:

-2x = 7

3. Divide both sides by -2:

x = -7/2

Example 4

Equation: 4x + 4 + 9x + 18 = 12(x + 2)

Solution Steps:

1. Distributing 12 on the right:

4x + 4 + 9x + 18 = 12x + 24

2. Rearranging the equation:

4x + 9x - 12x = 24 - 4 - 18

3. Combine like terms:

-13x = -22

4. Divide both sides by -13:

x = 2

Example 5

Equation: This example is slightly more complex and involves fractions.

Equation: (2/4)x + (3/7) = (1/3)(x + 9)

Solution Steps:

• First, eliminate the fractions by multiplying through by the least common multiple (LCM), which is 84 in this case:
• 84*(2/4)x + 84*(3/7) = 84*(1/3)(x + 9)

After simplifying, the equation becomes:

42x + 36 = 28(x + 9)

Now distribute:

42x + 36 = 28x + 252

Rearranging gives:

• 42x - 28x = 252 - 36
• 14x = 216
• x = 216/14

Verifying solutions

It's essential to verify your solutions to ensure accuracy. Here, we will check our previous examples:

Verification for Example 1

Substituting x = 2 into the original equation:

20 – 7(2) = 6(2) – 6

20 – 14 = 12 – 6

6 = 6 (True)

Verification for Example 2

Substituting x = -1:

7(-1) + 2 = 10(-1) + 5

-7 + 2 = -10 + 5

-5 = -5 (True)

Verification for Example 3

Substituting x = -7/2:

6(-7/2) - 5 = 8(-7/2) + 2

-21 - 5 = -28 + 2

-26 = -26 (True)

Common mistakes when solving linear equations

When solving linear equations, students often make several common errors. Here are some to watch out for:

• Forgetting to distribute: When there are parentheses, always remember to distribute correctly.
• Combining terms incorrectly: Ensure that you only combine like terms to avoid mistakes.
• Not isolating the variable: The goal is to get the variable by itself on one side of the equation.

Practice problems

To solidify your understanding, try these practice problems on your own:

• 1. 15 + 2x = 5x – 3
• 2. 3x + 4 = 7x – 8
• 3. 2(x + 5) = 3(x - 4)
• 4. (1/2)x + 3 = (2/3)(x + 9)
• 5. 5(2x - 3) = 3(x + 4)

Resources for further learning

If you want to deepen your understanding of linear equations, consider the following resources:

• Khan Academy: Linear Equations
• Math is Fun: Linear Equations
• Purplemath: Solving Linear Equations

Conclusion

As you can see, solving linear equations requires practice and attention to detail. By going through various examples and understanding common pitfalls, you can improve your problem-solving skills. Remember to practice regularly and use the resources available to you. Happy solving!

• Acerca de
• Últimas entradas

Sígueme

Sergio Ruiz

Consultor Educativo en Sergio Ruiz

Soy Director Universitario, consultor en estrategia educativa y copywriter especializado en instituciones que buscan crecer con visión, no por inercia. Cuento con más de 20 años liderando posgrados, diseñando modelos académicos orientados al mercado laboral y optimizando la rentabilidad institucional sin comprometer la calidad educativa.

He colaborado con universidades privadas en Latinoamérica, liderando iniciativas de captación, retención, empleabilidad y transformación digital. Como escritor, traduzco estrategias educativas en mensajes claros, persuasivos y accionables.

Combino experiencia académica, pensamiento estratégico y enfoque en resultados. Aquí comparto ideas para instituciones que quieren adaptarse al futuro… antes de que el futuro las arrase.

📬 ¿Quieres transformar tu institución o afinar tu mensaje educativo?
Hablemos.

Sígueme

Últimas entradas de Sergio Ruiz (ver todo)

• Domain and range of an algebraic function - octubre 28, 2026
• How to Calculate Percentages Effectively - octubre 28, 2026
• Understanding the concept of algebraic function - octubre 28, 2026

Si quieres conocer otros artículos parecidos a Solved Linear Equation Examples puedes visitar la categoría Math.