EQUAÇÃO DO 1º GRAU #04 RESOLUÇÃO DE EXERCÍCIOS | MATEMÁTICA BÁSICA |

Introduction

This tutorial aims to provide a clear and concise guide on solving first-degree equations, also known as linear equations. Understanding how to solve these equations is vital as they are commonly used in everyday problem-solving scenarios. We will break down the concepts and steps involved, ensuring that you can confidently tackle various exercises related to first-degree equations.

Step 1: Understanding the Components of an Equation

• An equation consists of:
  • Numbers: These are the constants in the equation.
  • Operations: Such as addition, subtraction, multiplication, and division.
  • Variables: Represented by letters (often x) that denote unknown values.
  • Equality Sign: Indicates that both sides of the equation are balanced.

Practical Tip

Visualize an equation like a balance scale; whatever you do to one side must also be done to the other to maintain balance.

Step 2: Setting Up the Equation

• Start with a word problem or statement that you need to convert into an equation.
• Identify the unknown variable and assign it a letter (commonly x).
• Translate the problem into a mathematical expression that equals a number.

Example

From the statement "Three times a number increased by four equals ten," you can set up the equation:

3x + 4 = 10

Step 3: Isolating the Variable

To solve for the variable, you need to isolate it on one side of the equation. Follow these steps:

1. Subtract or add terms on both sides as needed to move constants away from the variable.
   • Example: From 3x + 4 = 10, subtract 4 from both sides:

   3x = 6
   

2. Divide or multiply to solve for the variable.
   • Example: Divide both sides by 3:

   x = 2
   

Common Pitfall

Be careful with your operations; ensure you perform the same operation on both sides to maintain the balance.

Step 4: Checking Your Solution

Always verify your solution by substituting the variable back into the original equation to see if both sides are equal.

• For our example, substitute x back:

3(2) + 4 = 10
6 + 4 = 10

Since both sides are equal, the solution is confirmed.

Step 5: Practicing with Exercises

• Utilize the provided link to access a list of exercises to further practice solving first-degree equations:
  • Exercise List

Practical Tip

Start with simpler equations and gradually move to more complex ones as you gain confidence.

Conclusion

In this tutorial, we've covered the fundamental aspects of solving first-degree equations, from understanding their components to isolating the variable and verifying solutions. By practicing these steps, you will enhance your problem-solving skills in mathematics. For further learning, consider exploring additional resources and exercises to solidify your understanding. Happy studying!