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

Math with Mr. J
26 Jan 202006:54

TLDRIn this 'Math with Mr. J' video, the host explains how to solve one-step equations by performing the inverse operation to isolate the variable. Six problems are demonstrated, illustrating the process of undoing subtraction or division to find the variable's value. The importance of balancing the equation by applying the same operation to both sides is emphasized, and each solution is verified for accuracy.

Takeaways

  • 🔍 To solve one-step equations, perform the inverse operation of what is done to the variable to isolate it.
  • 📌 The main goal in solving equations is to get the variable by itself on one side of the equation.
  • ➕ For subtraction in the equation, the inverse operation is addition.
  • ➗ When the variable is divided by a number, the inverse operation is multiplication by that number.
  • 🔢 In the first example, adding six to both sides of the equation X - 6 = 13 results in X = 19.
  • 🧩 For the second problem, multiplying both sides of K / 8 = 2 by 8 gives K = 16.
  • 📉 In the third example, subtracting 3 from both sides of the equation 3 + G = 16 leads to G = 13.
  • 📈 In the fourth example, dividing both sides of 15 = 5M by 5 results in M = 3.
  • 🔄 For the fifth problem, dividing both sides of 2R = 22 by 2 gives R = 11.
  • 📊 In the sixth example, multiplying both sides of 11 = W / 4 by 4 results in W = 44.
  • 🔄 Remember to always double-check your solution by substituting the found value back into the original equation to ensure correctness.

Q & A

  • What is the main goal when solving one-step equations according to Mr. J's video?

    -The main goal when solving one-step equations is to get the variable by itself.

  • What is the hint provided at the beginning of the video for solving one-step equations?

    -The hint is to do the opposite or inverse operation of whatever is being done to the variable in order to isolate it.

  • How does the concept of inverse operations apply to solving equations in the video?

    -Inverse operations apply by doing the opposite of the operation performed on the variable, such as adding if the variable is subtracted, or multiplying if the variable is divided.

  • What is the first step in solving the equation X - 6 = 13 in the video?

    -The first step is to add six to both sides of the equation to isolate the variable X.

  • How does the video demonstrate the solution for the equation K ÷ 8 = 2?

    -The video shows that by multiplying both sides of the equation by 8, you can isolate K and find that K equals 16.

  • What is the process to solve the equation G + 3 = 16 as shown in the video?

    -The process involves subtracting 3 from both sides of the equation to isolate G and find that G equals 13.

  • In the video, how is the equation 15 = 5M solved?

    -The equation is solved by dividing both sides by 5 to isolate M and find that M equals 3.

  • What is the method used in the video to solve the equation 2R = 22?

    -The method involves dividing both sides by 2 to isolate R and find that R equals 11.

  • How does Mr. J solve the equation 11 = W ÷ 4 in the video?

    -Mr. J solves it by multiplying both sides by 4 to isolate W and find that W equals 44.

  • What is the importance of double-checking the solution in the video?

    -Double-checking the solution ensures that the steps taken to isolate the variable are correct and the final answer is accurate.

  • Why is it necessary to perform the same operation on both sides of the equation in the video?

    -Performing the same operation on both sides is necessary to maintain the balance of the equation and ensure the solution is valid.

Outlines

00:00

📚 Solving One-Step Equations Introduction

This paragraph introduces a math tutorial by Mr. J focusing on solving one-step equations. Six problems are presented on the screen, and the key concept emphasized is performing the inverse operation to isolate the variable. The tutorial explains that inverse operations involve doing the opposite of what is done to the variable, such as adding when there is subtraction and multiplying when there is division. The first problem, X minus six, is used as an example to demonstrate the process of isolating the variable by adding six to both sides of the equation, resulting in X equals 19. The solution is verified by substituting the value back into the original equation.

05:03

🔍 Detailed Walkthrough of Solving One-Step Equations

The second paragraph continues the tutorial by solving additional one-step equations. It covers various operations including division, multiplication, and addition. For each equation, the inverse operation is identified and applied to both sides to isolate the variable. For instance, the equation K divided by 8 equals 2 is solved by multiplying both sides by 8, yielding K equals 16. The tutorial also includes a step-by-step solution for equations involving multiplication, such as 2R equals 22, solved by dividing both sides by 2 to get R equals 11. Each solution is verified by substituting the variable's value back into the original equation to confirm its correctness. The final equation, 11 equals W divided by 4, is solved by multiplying both sides by 4 to find W equals 44, which is also verified for accuracy.

Mindmap

Keywords

💡One-Step Equations

One-step equations are algebraic equations that can be solved in a single operation. They are fundamental in teaching the process of solving equations and are characterized by having only one variable and one operation to undo. In the video, Mr. J demonstrates how to solve these equations by performing the inverse operation to isolate the variable. For example, if the variable is subtracted by a number, the inverse operation, which is addition, is used to solve for the variable.

💡Inverse Operation

An inverse operation is the mathematical action that 'undoes' another operation. In the context of solving one-step equations, if an operation such as addition or multiplication is applied to a variable, the inverse operation—subtraction or division, respectively—is used to isolate the variable. The video emphasizes the importance of performing the inverse operation to solve for the variable, as seen when Mr. J reverses subtraction with addition and division with multiplication.

💡Variable

A variable in algebra is a symbol, usually a letter, that represents an unknown value. The main goal when solving equations is to determine the value of the variable. In the script, Mr. J's objective in each problem is to manipulate the equation to get the variable by itself, which allows for finding the solution to the equation. For instance, in the equation 'X - 6 = 13', the variable is 'X', and the process involves adding 6 to both sides to isolate 'X' and find its value.

💡Equation Balance

Maintaining the balance of an equation is crucial when solving for a variable. Whatever operation is performed on one side of the equation must be performed on the other side to keep the equation equal. In the video, Mr. J consistently applies this principle, such as adding 6 to both sides of the equation 'X - 6 = 13' to maintain balance and ultimately solve for 'X'.

💡Multiplication

Multiplication is one of the basic arithmetic operations and is used in algebra to represent the repeated addition of a number. In the context of the video, multiplication is an operation that is performed on the variable, and its inverse, division, is used to isolate the variable. For example, in the equation '5M = 15', the variable 'M' is multiplied by 5, and dividing both sides by 5 is the method used to solve for 'M'.

💡Division

Division is the arithmetic operation of dividing a number into equal parts. In algebra, it is used to distribute a total into a number of groups. In the video, division is presented as an operation that needs to be reversed to solve for a variable. For instance, in the equation 'K / 8 = 2', the variable 'K' is divided by 8, and multiplying both sides by 8 is the inverse operation that isolates 'K'.

💡Addition

Addition is the process of combining two or more numbers to find their total or sum. In the video, when a variable is subtracted by a number, addition is used as the inverse operation to solve the equation. An example from the script is 'X - 6 = 13', where adding 6 to both sides helps isolate 'X' and find its value.

💡Subtraction

Subtraction is the arithmetic operation of taking one number away from another. In algebra, it can be an operation applied to a variable. The inverse of subtraction, which is addition, is used to isolate the variable in an equation. In the script, Mr. J uses addition to reverse the subtraction in equations like 'X - 6 = 13'.

💡Double Check

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. In the video, Mr. J emphasizes the importance of this step to confirm the correctness of the solution. For example, after finding 'X = 19', he substitutes it back into the equation 'X - 6 = 13' to verify that '19 - 6' indeed equals '13'.

💡Algebra

Algebra is a branch of mathematics that uses symbols and the rules of operations to manipulate and solve equations. In the video, algebraic principles are applied to solve one-step equations. The process involves understanding and applying operations such as addition, subtraction, multiplication, and division to isolate variables and find their values, as demonstrated through the various examples provided by Mr. J.

Highlights

Introduction to solving one-step equations with six example problems.

The importance of performing the inverse operation to isolate the variable.

Explanation of 'inverse' as the opposite operation, such as subtraction for addition.

Solving the first equation by adding six to both sides to isolate X.

Verification of the solution by substituting the value back into the equation.

Approach to the second problem involving division and multiplication.

Isolating the variable K by multiplying both sides by 8.

Third problem's strategy of subtracting 3 from both sides to solve for G.

Rewriting the equation with the variable first for clarity.

Solving the fourth equation by dividing both sides by 5 to find M.

Understanding the multiplication sign next to a variable and its inverse operation.

Fifth problem's method of dividing by 2 to isolate R.

Verification of the solution by checking the multiplication of the variable's value.

Sixth problem involves dividing by 4 and the inverse operation of multiplication.

Final solution for W by multiplying both sides by 4 and verification.

Summary of the process for solving one-step equations with practical examples.

Emphasis on the importance of keeping the equation balanced by performing operations on both sides.

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