How to Solve One-Step Equations | One-Step Equation Steps | Math with Mr. J

Math with Mr. J
26 Jan 202006:54

TLDRIn 'Math with Mr. J', the video focuses on solving one-step equations by performing the inverse operation to isolate the variable. The tutorial covers six problems, demonstrating how to undo subtraction and division to find the variable's value. Key takeaways include adding or multiplying the inverse operation to both sides of the equation to maintain balance and checking solutions for accuracy. The methodical approach ensures a clear understanding of solving basic algebraic equations.

Takeaways

  • 📘 To solve one-step equations, perform the inverse operation on the variable to isolate it.
  • 🔢 For an equation like 'X - 6 = 13', add 6 to both sides to find X = 19.
  • ➗ In 'K ÷ 8 = 2', multiply both sides by 8 to get K = 16.
  • 🔄 When the variable is on the right, like '3 + G = 16', perform the opposite operation on both sides to solve for G.
  • 📉 For equations involving multiplication, such as '5M = 15', divide both sides by 5 to find M = 3.
  • 🔄 In '2R = 22', divide both sides by 2 to get R = 11.
  • 🔢 To solve '11 = W ÷ 4', multiply both sides by 4 to find W = 44.
  • ✅ Always double-check your answer by substituting it back into the original equation to ensure it's correct.
  • 📐 The goal of solving one-step equations is to isolate the variable by performing the opposite operation to what's done to it in the equation.

Q & A

  • What is the main goal when solving one-step equations?

    -The main goal is to get the variable by itself by doing the opposite or inverse operation of whatever is being done to the variable.

  • What does 'inverse' mean in the context of solving equations?

    -In the context of solving equations, 'inverse' means to do the opposite operation. For example, the inverse of addition is subtraction, and the inverse of multiplication is division.

  • How do you solve the equation X - 6 = 13?

    -To solve X - 6 = 13, you add 6 to both sides of the equation to isolate X, resulting in X = 19.

  • What is the process to check if the solution to X - 6 = 13 is correct?

    -To check if the solution is correct, you substitute X with 19 and verify if 19 - 6 equals 13, which it does, confirming the solution is correct.

  • How do you approach an equation where the variable is divided by a number?

    -If the variable is divided by a number, you multiply both sides of the equation by that number to isolate the variable.

  • What is the solution to the equation K / 8 = 2?

    -To solve K / 8 = 2, you multiply both sides by 8, resulting in K = 16.

  • Why is it important to do the same operation to both sides of an equation?

    -It is important to do the same operation to both sides of an equation to maintain the balance and ensure the equality holds true.

  • How do you solve an equation where a number is added to a variable?

    -To solve an equation where a number is added to a variable, you subtract that number from both sides to isolate the variable.

  • What is the solution to the equation 15 = 5M?

    -To solve 15 = 5M, you divide both sides by 5, resulting in M = 3.

  • How do you handle an equation where the variable is multiplied by a number?

    -If the variable is multiplied by a number, you divide both sides by that number to isolate the variable.

  • What is the solution to the equation 2R = 22?

    -To solve 2R = 22, you divide both sides by 2, resulting in R = 11.

  • How do you solve an equation where the variable is divided by a number and the result is equal to another number?

    -To solve an equation like 11 = W / 4, you multiply both sides by 4 to isolate W, resulting in W = 44.

Outlines

00:00

📘 Introduction to Solving One-Step Equations

This paragraph introduces the topic of solving one-step equations with Mr. J. The instructor presents six problems on the screen and emphasizes the importance of performing the inverse operation to isolate the variable. The concept of inverse operations is explained, where addition's inverse is subtraction and multiplication's inverse is division. The instructor then proceeds to solve the first problem step by step, demonstrating how to add six to both sides of the equation to isolate the variable X, resulting in X = 19. The solution is verified by substituting the value back into the original equation.

05:03

🔢 Solving More One-Step Equations

In the second paragraph, the instructor continues with more one-step equation problems. The method of isolating the variable through inverse operations is applied to various scenarios: multiplying by 8 to solve for K, subtracting 3 to solve for G, dividing by 5 to solve for M, dividing by 2 to solve for R, and multiplying by 4 to solve for W. Each solution is checked by substituting the found value back into the original equation to ensure its correctness. The paragraph concludes with a summary of the process and a confirmation that all solutions are accurate, reinforcing the method of solving one-step equations.

Mindmap

Keywords

💡One-Step Equations

One-step equations are algebraic equations that can be solved in a single operation. They typically involve a simple arithmetic operation such as addition, subtraction, multiplication, or division applied to the variable. In the video, Mr. J demonstrates how to solve these equations by performing the inverse operation to isolate the variable. For example, if the equation is 'X - 6 = 13', the inverse operation, which is addition, is applied to both sides to get 'X = 19'.

💡Inverse Operation

Inverse operations are mathematical processes that undo the effect of another operation. In the context of solving one-step equations, the inverse operation is used to cancel out the operation done to the variable, allowing it to be isolated. The video emphasizes that if the variable is being subtracted, you add; if it's being multiplied, you divide, and so on. For instance, to solve 'X - 6 = 13', the inverse operation of addition (+6) is applied to both sides to isolate 'X'.

💡Variable

A variable in algebra represents an unknown value that can change. It is usually denoted by a letter such as 'X', 'K', or 'M'. The main goal when solving equations is to determine the value of the variable. In the video, Mr. J shows how to manipulate equations to get the variable by itself on one side of the equation, which is essential for finding its value.

💡Equation Balance

Equation balance refers to the property that both sides of an equation must remain equal after any operation is performed. This is a fundamental principle in algebra, ensuring that the equation's validity is maintained throughout the solving process. In the script, Mr. J adds or multiplies both sides of the equation to keep it balanced, such as adding 6 to both sides in the equation 'X - 6 = 13'.

💡Solving Equations

Solving equations involves finding the value of the variable that makes both sides of the equation equal. The video provides a step-by-step guide on how to solve one-step equations by using inverse operations. Each example in the video illustrates a different scenario where an equation is solved, such as finding 'X = 19' from 'X - 6 = 13'.

💡Double-Checking

Double-checking is the process of verifying the solution to an equation by substituting the found value of the variable back into the original equation to ensure it holds true. This is a crucial step in solving equations to confirm accuracy. In the video, Mr. J demonstrates double-checking by substituting 'X = 19' back into 'X - 6 = 13' and confirming that '19 - 6 = 13' is correct.

💡Multiplication

Multiplication is one of the basic arithmetic operations used in algebraic equations. In the context of the video, multiplication is an operation that may be applied to a variable, and its inverse operation, division, is used to isolate the variable. For example, in the equation '5M = 15', division by 5 is the inverse operation to solve for 'M'.

💡Division

Division is the arithmetic operation of finding an unknown factor when the product of that factor and another number is known. In algebra, division is often used as an inverse operation to undo multiplication. The video shows how division is used to solve equations like '15 = 5M', where dividing both sides by 5 isolates 'M'.

💡Algebra

Algebra is a branch of mathematics that uses symbols and the rules of arithmetic to perform calculations and solve for unknowns. The video focuses on a fundamental aspect of algebra: solving one-step equations. It provides practical examples of how algebraic principles are applied to find the values of variables in simple equations.

💡Math with Mr. J

Math with Mr. J is presumably the name of the educational series or the specific video where these concepts are being taught. It implies an approachable and instructional style, aiming to make learning algebra more accessible. The video script suggests that Mr. J uses clear examples and step-by-step instructions to teach viewers how to solve one-step equations.

Highlights

Introduction to solving one-step equations with Mr. J.

Key hint: Perform the inverse operation to isolate the variable.

Inverse operations: Addition's inverse is subtraction, multiplication's inverse is division.

Example 1: Solving X - 6 = 13 by adding 6 to both sides.

Verification: Checking if 19 - 6 equals 13.

Example 2: Solving K / 8 = 2 by multiplying both sides by 8.

Verification: Confirming 16 / 8 equals 2.

Example 3: Isolating G by subtracting 3 from both sides.

Verification: Ensuring 3 + 13 equals 16.

Example 4: Solving 15 = 5M by dividing both sides by 5.

Verification: Checking if 5 * 3 equals 15.

Example 5: Solving 2R = 22 by dividing both sides by 2.

Verification: Confirming 2 * 11 equals 22.

Example 6: Solving 11 = W / 4 by multiplying both sides by 4.

Verification: Ensuring 44 / 4 equals 11.

Summary of solving one-step equations by performing inverse operations.

Emphasis on balancing the equation by performing operations on both sides.

Importance of verifying the solution to ensure accuracy.

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