Solving One-Step Equations | Expressions & Equations | Grade 6

Math is Simple!
31 Aug 202004:21

TLDRIn this video, we explore the addition property of equality, which is crucial for solving one-step equations. The key principle is that whatever operation is performed on one side of the equation must be done on the other to maintain balance. The video demonstrates how to add the inverse of a number to isolate the variable, solve for it, and then check the solution for accuracy. Two examples are shown, where the process is applied step-by-step, emphasizing the importance of checking your work to ensure correctness.

Takeaways

  • ➕ When solving one-step equations, apply the same operation to both sides of the equation to maintain balance.
  • ❓ Identify the number attached to the variable and understand how it interacts with the variable (e.g., negative or positive).
  • 🔄 The inverse operation helps cancel out terms (e.g., adding positive 5 to cancel negative 5).
  • 🧮 After performing the operation, simplify the equation and solve for the variable.
  • ✏️ Drop terms that equal zero (e.g., m + 0 becomes m).
  • 🔢 In the first example, the equation simplifies to m = 14 after adding 5 to both sides.
  • ➕ In the second example, adding 12 to both sides cancels out negative 12, simplifying the equation to b = 29.
  • ✅ Always double-check your work by substituting the solution back into the original equation.
  • 🔄 Use inverse operations to verify that both sides of the equation are equal after substitution.
  • 💡 Remember, one-step equations are solved by applying the same operation on both sides using the addition property of equality.

Q & A

  • What is the addition property of equality?

    -The addition property of equality states that whatever you add to one side of an equation, you must also add to the other side to maintain the equality.

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

    -It's important to do the same operation on both sides to maintain the balance of the equation and ensure the equality remains true.

  • In the first example, what is the variable and what number is attached to it?

    -In the first example, the variable is 'm' and the number attached to it is -5.

  • What is the inverse of -5 in the first example?

    -The inverse of -5 is +5.

  • What operation is performed to solve for the variable in the first equation?

    -To solve for the variable, +5 is added to both sides of the equation.

  • How does adding 5 on both sides simplify the equation in the first problem?

    -Adding 5 on both sides cancels out the -5, leaving only the variable 'm' on one side and simplifying the other side to 14.

  • What is the solution to the first equation?

    -The solution to the first equation is m = 14.

  • In the second example, what is the variable and what number is attached to it?

    -In the second example, the variable is 'b' and the number attached to it is -12.

  • What is the solution to the second equation?

    -The solution to the second equation is b = 29.

  • Why is it important to check your work when solving equations?

    -Checking your work ensures that the solution is correct and that both sides of the equation are equal after substituting the variable's value.

Outlines

00:00

🧮 Introduction to the Addition Property of Equality

This paragraph introduces the addition property of equality. It explains that when solving one-step equations, what is done to one side of the equation must be done to the other side. This maintains the balance of the equation. The first example involves the variable 'm' and negative 5. By adding 5 to both sides, the equation simplifies to m = 14. This demonstrates how the addition property is used to solve simple equations.

🔄 Solving the Second One-Step Equation

The second paragraph explores a similar one-step equation with the variable 'b' and negative 12. The variable and constant are in reverse order, but the approach remains the same. By adding 12 to both sides, the equation simplifies to b = 29. The steps remain consistent with the addition property, where the same operation is applied on both sides of the equation.

✔️ Double-Checking the Solutions

This paragraph emphasizes the importance of checking your work after solving equations. The speaker substitutes the solved values of the variables back into the original equations to confirm the accuracy of the solutions. Both checks, m = 14 and b = 29, are shown to be correct by substituting these values back into their respective equations and verifying that both sides are equal.

📝 Key Takeaways from the Lesson

The final part of the video script reinforces the core principle of the addition property of equality. The speaker reminds viewers that what is done on one side of the equation must be done on the opposite side to maintain balance. This method applies to solving one-step equations, which are straightforward to handle by following the steps outlined.

Mindmap

Keywords

💡Addition Property of Equality

This property states that if you add the same value to both sides of an equation, the equality remains true. In the video, it's applied to solve one-step equations, ensuring that the equation remains balanced while isolating the variable.

💡One-Step Equations

These are equations that can be solved in a single step, typically by adding, subtracting, multiplying, or dividing. In the video, examples include adding 5 to both sides or subtracting a constant to solve for the variable.

💡Variable

A symbol, usually a letter, that represents an unknown value in an equation. In the video, variables like 'm' and 'b' are isolated to find their value by using inverse operations on both sides of the equation.

💡Inverse Operations

Operations that undo each other, such as addition and subtraction or multiplication and division. The video uses inverse operations to simplify equations, like adding 12 to cancel out negative 12 and solve for 'b'.

💡Negative and Positive Numbers

Numbers below and above zero, respectively. In the video, operations involving negative and positive numbers are key in solving equations, such as adding positive 5 to cancel out negative 5.

💡Check Your Work

A process to verify the solution by substituting the value of the variable back into the original equation. The video demonstrates this by plugging values back into the equations to ensure both sides remain equal.

💡Constant

A fixed number in an equation that does not change. The video shows constants like -5 or -12, which are added or subtracted to isolate the variable and solve the equation.

💡Integrity of the Equal Sign

Maintaining balance on both sides of the equation during operations. The video emphasizes that whatever is done to one side of the equation must be done to the other to preserve this integrity.

💡Combining Integers

Adding or subtracting integers (positive and negative whole numbers). The video shows examples like adding 29 positives and 12 negatives to get a result of 17.

💡Simplify

To reduce an equation to its simplest form, usually by performing operations that eliminate terms or constants. In the video, equations are simplified by canceling out numbers and dropping unnecessary zeros to reveal the value of the variable.

Highlights

Introduction to the addition property of equality.

Emphasizes the importance of maintaining the integrity of the equal sign.

Explanation of how to solve one-step equations by performing the same operation on both sides of the equation.

Describes how to isolate the variable by recognizing what number is attached to it.

Shows that the inverse of a negative number is a positive number.

Addition of 5 to both sides of the equation as a demonstration.

Negative five and positive five are inverses, making the result zero.

Final solution for the first problem: m equals 14.

Approach to solving a second one-step equation, even when the variable and constant are in reverse order.

Identifying negative 12 as the number attached to the variable b.

Adding 12 to both sides as the inverse of negative 12.

Solution for the second problem: b equals 29.

Double-checking solutions by substituting the values back into the original equations.

Explanation of how combining positive and negative integers checks the solution.

Reinforcement of the principle: What you do on one side of the equation must be done on the other.

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