EQUAÇÃO DO 1º GRAU COM DISTRIBUTIVA \Prof. Gis/

Summary

In this engaging math lesson, the teacher explains how to solve first-degree equations by using the distributive property. Through step-by-step examples, students are guided in simplifying equations, applying multiplication, and understanding the rules of signs (positive and negative numbers). The teacher emphasizes the importance of prior concepts, breaking down the problem-solving process with clear instructions and encouragement. With interactive examples and tips for mental calculations, this lesson makes learning algebra approachable and fun, while motivating students to apply the concepts in their exercises.

Takeaways

• 😀 Equations of the first degree involve an unknown variable (usually represented by 'x') and an equality sign, indicating that both sides of the equation are equal.
• 😀 The distributive property states that when a number is multiplied by a sum or difference inside parentheses, it should be multiplied by each term separately.
• 😀 To solve equations with parentheses, first apply the distributive property, multiplying the term outside the parentheses by each term inside.
• 😀 In solving equations, always isolate the variable (e.g., 'x') on one side of the equation by moving terms with numbers to the opposite side.
• 😀 When moving a term across the equal sign, reverse its operation: for example, if a term is added to one side, subtract it from the other side.
• 😀 The operation that 'undoes' multiplication is division. If a variable is multiplied by a number, divide both sides of the equation by that number to isolate the variable.
• 😀 When multiplying negative numbers, remember the rule: a positive times a negative gives a negative result.
• 😀 Simplifying equations involves combining like terms, such as adding or subtracting terms with the same variable.
• 😀 When the division of terms does not result in a whole number, express the result as a fraction, often simplified to its lowest terms.
• 😀 Practice is key in solving equations. Use mental math strategies for quick calculations, like breaking down multiplication into smaller steps (e.g., 5x12 as 5x10 + 5x2).

Q & A

What is a first-degree equation, as explained in the video?

A first-degree equation is an equation that contains an unknown variable (typically represented by a letter like 'x') and involves only first-degree terms, meaning the variable is not raised to any power other than one. It also includes an equality sign (i.e., '=').

How do you apply the distributive property when solving equations?

The distributive property is applied by multiplying the number outside the parentheses by each term inside the parentheses. For example, if you have '3(x + 6)', you multiply '3' by 'x' and '3' by '6', resulting in '3x + 18'.

What is the role of parentheses in an equation?

Parentheses indicate that the terms inside them must be handled first, often requiring the distributive property to simplify the equation. They help organize the operations and show which terms are grouped together.

What happens when a negative number is outside parentheses in an equation?

When a negative number is outside parentheses, it affects the signs of the terms inside the parentheses. For example, '-5(x + 12)' becomes '-5x - 60' because you distribute the negative sign to each term inside the parentheses.

How do you handle terms with variables when simplifying equations?

Terms with variables are grouped together on one side of the equation, while constants (numbers without variables) are moved to the other side. This helps isolate the variable for easy solving.

What is the process for solving a first-degree equation after applying the distributive property?

After applying the distributive property, you combine like terms, move all variable terms to one side and constant terms to the other side, then solve for the variable using basic operations like addition, subtraction, multiplication, or division.

What is meant by 'transporting' terms in the equation?

'Transporting' terms refers to moving terms from one side of the equation to the other, changing their sign. For instance, if a term is negative on the left side, it becomes positive when moved to the right side.

How do you handle division when solving for a variable?

When a number is multiplying the variable, you perform the inverse operation, which is division, to isolate the variable. For example, if '3x = 27', you divide both sides by 3 to solve for 'x'.

What does the rule of signs explain when multiplying or dividing numbers?

The rule of signs states that when multiplying or dividing numbers, if the signs are the same (both positive or both negative), the result is positive. If the signs are different (one positive, one negative), the result is negative.

How do you simplify fractions in an equation?

To simplify fractions, you divide both the numerator and the denominator by their greatest common divisor. For example, 86/14 can be simplified by dividing both by 2, resulting in 43/7.