Solving Two-Step Equations | Expressions & Equations | Grade 7

Math is Simple!
14 Apr 202003:40

TLDRThis educational video teaches viewers how to solve two-step equations, a fundamental algebra skill. The presenter uses the example 7x + 3 = 38, demonstrating how to isolate the variable 'x' by performing inverse operations. First, subtracting 3 from both sides to eliminate the constant term, then dividing by 7 to solve for 'x'. The solution, x = 5, is verified by substituting it back into the original equation. The video emphasizes the importance of checking work to ensure accuracy, providing a clear and concise guide for Grade 7 students learning expressions and equations.

Takeaways

  • 🔢 Solving two-step equations involves manipulating the equation to isolate the variable.
  • 📘 The first step often involves dealing with constants or coefficients attached to the variable.
  • ➕ To remove a constant from the left side, apply its inverse operation (subtraction) to both sides of the equation.
  • 🔄 After the first step, check the equation to ensure the variable is still correctly represented.
  • 📉 If the variable is multiplied by a number, use division as the inverse operation to isolate it.
  • 🧐 Always perform the same operation on both sides of the equation to maintain equality.
  • 🔍 After finding the solution, it's crucial to check the work by substituting the variable's value back into the original equation.
  • 📊 The verification process confirms if the solution satisfies the original equation by ensuring both sides are equal.
  • 📐 The goal is to simplify the equation to the point where the variable is by itself, indicating the correct solution.
  • 🎓 Understanding the inverse operations (additive inverse for constants, multiplicative inverse for coefficients) is key to solving two-step equations.
  • 📝 The process emphasizes the importance of both solving and verifying the solution to ensure accuracy.

Q & A

  • What is a two-step equation?

    -A two-step equation is an algebra equation that requires two steps to find the final solution.

  • How do you approach solving a two-step equation?

    -To solve a two-step equation, you manipulate the equation to isolate the variable by itself on one side of the equation.

  • What is the first step in solving the equation 7x + 3 = 38?

    -The first step is to eliminate the constant term attached to the variable by performing the inverse operation, which in this case is subtracting 3 from both sides.

  • What is the inverse operation of adding 3?

    -The inverse operation of adding 3 is subtracting 3.

  • After the first step, what is the simplified form of the equation 7x + 3 = 38?

    -After subtracting 3 from both sides, the simplified form is 7x = 35.

  • How do you isolate x in the equation 7x = 35?

    -To isolate x, you divide both sides of the equation by 7, which is the coefficient of x.

  • What is the solution to the equation 7x = 35 after performing the second step?

    -After dividing both sides by 7, the solution is x = 5.

  • How can you check if your solution to a two-step equation is correct?

    -You can check your solution by substituting the value of x back into the original equation and verifying that both sides are equal.

  • What is the final answer to the equation 7x + 3 = 38 after checking your work?

    -The final answer is x = 5, which is verified by substituting it back into the equation and confirming that 7(5) + 3 equals 38.

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

    -Checking your work ensures that the solution is correct and helps identify any mistakes made during the solving process.

  • What is the general process for solving two-step equations as described in the script?

    -The general process involves manipulating the equation to isolate the variable, finding the solution, and then checking the work to confirm the solution is correct.

Outlines

00:00

📘 Solving Two-Step Equations

This paragraph introduces the concept of two-step equations in algebra, which are equations that require two operations to isolate the variable. The example given is 7x + 3 = 38. The process involves first subtracting 3 from both sides to get 7x = 35, and then dividing both sides by 7 to isolate x, resulting in x = 5. The paragraph emphasizes the importance of checking the solution by substituting the value of x back into the original equation to ensure both sides balance, confirming x = 5 as the correct solution.

Mindmap

Keywords

💡Two-Step Equations

Two-step equations are algebraic equations that require two main operations to isolate the variable and find its value. In the context of the video, the term refers to the process of solving equations that involve first eliminating a constant or coefficient from one side of the equation and then performing another operation to solve for the variable. An example from the script is the equation '7x + 3 = 38', where the first step is to eliminate the '+3' by subtracting 3 from both sides, and the second step is to divide both sides by 7 to solve for x.

💡Manipulate the Equation

Manipulating the equation involves performing mathematical operations to transform the equation in a way that isolates the variable. This is a key step in solving algebraic equations. In the video, the term is used to describe the process of moving terms from one side of the equation to the other to simplify and solve for the variable. For instance, to isolate 'x' in '7x + 3 = 38', the '+3' is manipulated to the other side by performing the inverse operation, which is subtraction.

💡Inverse Operation

The inverse operation is a mathematical process that undoes the effect of another operation. It is crucial in solving equations as it helps to cancel out terms. In the video, the inverse operation is used to eliminate the '+3' by subtracting 3 from both sides of the equation, effectively 'undoing' the addition of 3. This is a fundamental concept in algebra, allowing for the simplification of equations.

💡Isolate the Variable

Isolating the variable means getting the variable alone on one side of the equation, which is necessary to find its value. The video emphasizes this as the goal when solving two-step equations. It is illustrated in the script when the presenter moves the '+3' to the other side and then divides by 7 to leave 'x' by itself, ultimately finding that 'x = 5'.

💡Check Your Work

Checking your work is an important step in problem-solving to ensure the correctness of the solution. In the video, the presenter demonstrates how to verify the solution by substituting the found value of 'x' back into the original equation to see if both sides balance. This step confirms that the solution is accurate and helps in building confidence in the solving process.

💡Variable

A variable is a symbol, often a letter, that represents an unknown value in an equation. In algebra, variables are used to find specific values that satisfy the equation. The video's theme revolves around solving for the variable 'x' in the given equation. The script uses 'x' as the variable to demonstrate the process of solving two-step equations.

💡Coefficient

A coefficient is a numerical factor that multiplies a variable in an algebraic expression. In the script, the term is implicitly used when referring to the number '7' that is multiplied by 'x'. Understanding coefficients is essential for correctly performing operations on variables and solving equations.

💡Constant

A constant is a value that does not change during the solution process of an equation. In the context of the video, the '3' in the equation '7x + 3 = 38' is a constant, as it remains unchanged until it is manipulated to be eliminated from the equation. Constants are often the first terms to be dealt with when solving equations.

💡Division

Division is one of the fundamental operations in arithmetic, used to split a number into equal parts. In algebra, division is used to isolate variables by undoing multiplication. The video demonstrates division as the second step in solving the equation '7x = 35' by dividing both sides by 7 to find 'x'.

💡Subtraction

Subtraction is the arithmetic operation of removing one amount from another. In the video, subtraction is used as an inverse operation to eliminate the '+3' from the equation '7x + 3 = 38'. By subtracting 3 from both sides, the presenter shows how to simplify the equation and move closer to isolating the variable.

💡Balanced Equation

A balanced equation is one where both sides are equal, which is a requirement for the equation to be true. The video script mentions checking the solution by ensuring that the equation remains balanced after substituting the found value of 'x'. This confirms that the operations performed were correct and the solution is valid.

Highlights

Introduction to solving two-step equations in algebra.

Two-step equations require two operations to isolate the variable.

First example equation: 7x + 3 = 38.

Goal is to manipulate the equation to get x by itself.

Use inverse operations to move terms attached to x to the other side.

Subtract 3 from both sides to eliminate the constant term.

Resulting equation after subtraction: 7x = 35.

Divide both sides by 7 to solve for x.

Final solution: x = 5.

Checking work by substituting the solution back into the original equation.

Verification step: 7(5) + 3 = 38.

Confirming the solution by showing both sides of the equation are equal.

Emphasis on the importance of checking work for accuracy.

Summary of the process: manipulate the equation, solve for x, and check the work.

Reinforcement of the method for solving two-step equations.

Encouragement to practice to master the technique.

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