EQUAÇÃO DO 1º GRAU EM 6 MINUTOS

Summary

This video tutorial explains how to solve first-degree equations step-by-step. Through multiple examples, the speaker demonstrates key techniques like isolating the variable, applying the distributive property, and managing signs when moving terms across the equal sign. The tutorial also covers solving equations with fractions, negative coefficients, and instances where multiplication or division is needed. The video aims to simplify the process, offering clear, accessible methods for students to master solving linear equations and ensuring that each step is fully explained and understood.

Takeaways

• 😀 Isolate the variable (x) to solve for it in first-degree equations.
• 😀 When moving terms across the equality sign, change their signs (e.g., +4 becomes -4).
• 😀 Solve for x by performing arithmetic operations like addition, subtraction, multiplication, or division.
• 😀 Always check your solution by substituting the value of x back into the original equation.
• 😀 When dealing with fractions, cross-multiply to eliminate the denominators.
• 😀 Use parentheses when multiplying terms to avoid mistakes, especially when a term affects multiple parts of an equation.
• 😀 The distributive property can be used to simplify equations, especially when there are terms multiplying a binomial.
• 😀 In equations with negative variables (e.g., -x), multiply both sides by -1 to make the variable positive.
• 😀 Group like terms (e.g., all x terms together and all constant terms together) to simplify the equation.
• 😀 In cases where you have fractions or decimals, it’s often helpful to multiply through by a common denominator to eliminate them.
• 😀 Practice solving different types of equations to ensure a thorough understanding of the method.

Q & A

What is the objective when solving a first-degree equation like 2x + 4 = 10?

The objective is to find the value of x that makes the equation true. In this case, you isolate the term with x and solve for its value.

How do you isolate the term with the variable in the equation 2x + 4 = 10?

You isolate the term with x by moving the other terms to the opposite side of the equation. In this case, you subtract 4 from both sides to get 2x = 6.

Why do we change the sign when moving terms from one side of the equation to the other?

We change the sign to maintain the equality of the equation. When you move a positive number to the other side, it becomes negative, and vice versa.

What is the solution to the equation 2x = 6?

The solution is x = 3, because dividing both sides by 2 gives x = 6 ÷ 2 = 3.

In the equation 6x + 2x = 16, how do you combine like terms?

You combine the x terms by adding them together, so 6x + 2x becomes 8x, resulting in the equation 8x = 16.

What is the process for solving an equation like 5x - 4 = 6x + 8?

You move all the x terms to one side and all the constants to the other. Subtract 5x from both sides, and add 4 to both sides, resulting in -x = 12.

What should you do when you have a negative variable like -x in an equation?

You multiply both sides of the equation by -1 to make the variable positive. In this case, -x = 12 becomes x = -12.

How do you solve equations involving fractions, like 2x / -2 = 15 / 3?

You can solve this by multiplying both sides of the equation crosswise. This ensures that you eliminate the fractions and simplify the equation.

What does the distributive property do in equations like 2(x - 2)?

The distributive property allows you to multiply each term inside the parentheses by the term outside. For example, 2(x - 2) becomes 2x - 4.

How do you solve equations with terms on both sides, such as 2x - 3 = 6x - 2?

First, move the x terms to one side by subtracting 2x from both sides, and then move the constants to the other side. This simplifies the equation to -x = 12, which becomes x = -12 after multiplying by -1.