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

Math is Simple!
14 Apr 202003:40

TLDRThis educational video teaches how to solve two-step equations, a fundamental algebra skill for Grade 7. The presenter demonstrates solving the equation 7x + 3 = 38 by first isolating the term with the variable, then using inverse operations to isolate x. The process involves subtracting 3 from both sides to eliminate the constant, and then dividing by 7 to solve for x. The solution, x = 5, is verified by substituting back into the original equation. The video emphasizes the importance of checking work to ensure accuracy.

Takeaways

  • 📘 Solving two-step equations involves manipulating the equation in two steps to isolate the variable.
  • 🔱 The first step often involves eliminating the constant term attached to the variable by using its inverse operation.
  • ➕ In the example, subtracting 3 from both sides of the equation (7x + 3 = 38) helps to isolate the term with the variable.
  • ➖ After the first step, the equation becomes (7x = 35), moving closer to isolating the variable x.
  • 🔄 The second step involves dealing with the coefficient of the variable, using division as the inverse operation of multiplication.
  • 👉 Dividing both sides of the equation (7x = 35) by 7 results in (x = 5), finding the value of x.
  • 🔍 To verify the solution, substitute the found value of x back into the original equation to check if both sides balance.
  • 📈 The check involves performing the same operations on both sides of the equation to ensure the solution is correct.
  • 🎯 The final solution is confirmed when the substituted value of x makes both sides of the equation equal, proving the solution is accurate.
  • 📝 It's crucial to remember to perform the same operation on both sides of the equation to maintain equality.
  • 🔑 The process highlights the importance of checking work to ensure the accuracy of the solution in algebraic equations.

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 start solving a two-step equation?

    -You start by manipulating the equation to get the variable, typically 'x', by itself.

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

    -The first step is to isolate the term with the variable by performing the inverse operation of the number attached to the variable. In this case, subtracting 3 from both sides to eliminate the +3.

  • What is the inverse operation of addition?

    -The inverse operation of addition is subtraction.

  • After moving the +3 to the other side of the equation, what is the new equation?

    -After subtracting 3 from both sides, the new equation is 7x = 35.

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

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

  • What is the result of dividing both sides of the equation 7x = 35 by 7?

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

  • How do you check if your solution to the equation is correct?

    -You check the solution by substituting the value of 'x' back into the original equation and verifying that both sides of the equation balance.

  • What is the final solution to the equation 7x + 3 = 38?

    -The final solution is x = 5.

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

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

  • What is the general approach for solving two-step equations?

    -The general approach is to manipulate the equation to isolate the variable, solve for the variable, and then check the solution by substituting it back into the original equation.

Outlines

00:00

📘 Solving Two-Step Equations

This video segment teaches viewers how to solve two-step equations, which are algebraic equations that require two steps to isolate the variable. The example given is 7x + 3 = 38. The process involves manipulating the equation to isolate 'x' by performing inverse operations. In this case, subtracting 3 from both sides to eliminate the constant on the left side, resulting in 7x = 35. Then, dividing both sides by 7 to solve for 'x', yielding x = 5. The video 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 solve for the variable. In the context of the video, the term refers to the process of isolating the variable by performing two distinct steps, typically involving the manipulation of terms on both sides of the equation to simplify and solve for the unknown.

💡Manipulate

To manipulate in the context of algebra means to alter or adjust the terms in an equation to achieve a specific goal, such as isolating the variable. The video script illustrates this by showing how to move the constant term from one side of the equation to the other to isolate 'x'.

💡Inverse Operation

Inverse operations are mathematical processes that undo the effect of another operation. In the video, the concept is used to explain how to counteract an addition by performing subtraction, or how to counteract multiplication by performing division, in order to isolate the variable.

💡Isolate the Variable

Isolating the variable is the process of getting the variable alone on one side of the equation, which is a necessary step in solving algebraic equations. The video demonstrates this by showing how to eliminate constants and coefficients to leave 'x' by itself.

💡Coefficient

A coefficient is a numerical factor that multiplies a variable in an algebraic expression. In the video, the coefficient '7' is attached to 'x', and the process of removing it to solve for 'x' is explained through division.

💡Division

Division is one of the arithmetic operations used in the video to isolate the variable by undoing the multiplication. The script shows how dividing both sides of the equation by the coefficient of 'x' (which is 7) simplifies the equation to solve for 'x'.

💡Check Your Work

Checking your work is an essential step in problem-solving to ensure that the solution is correct. The video emphasizes the importance of verifying the solution by substituting the found value of 'x' back into the original equation to see if both sides balance.

💡Balanced Equation

A balanced equation is one where both sides are equal after the solution has been found. The video uses the term to describe the final state of the equation when the correct value of the variable has been determined and the equation holds true.

💡Variable

A variable in algebra represents an unknown quantity that can change. In the video, 'x' is the variable that the process of solving the two-step equation aims to determine.

💡Equation

An equation is a mathematical statement that asserts the equality of two expressions. The video focuses on solving equations that involve two steps of manipulation to find the value of the variable that makes the equation true.

💡Solution

The solution to an equation is the value of the variable that makes the equation true. The video script guides viewers through the process of finding this value for the variable 'x' in a two-step equation.

Highlights

Introduction to solving two-step equations in algebra.

A two-step equation requires two operations to isolate the variable.

The first example presented is 7x + 3 = 38.

The goal is to manipulate the equation to isolate x.

To remove the constant term, perform the inverse operation on both sides.

Subtract 3 from both sides to eliminate the constant term.

After subtraction, the equation becomes 7x = 35.

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

Division leads to x = 5 as the solution.

Checking the solution involves substituting the value of x back into the original equation.

Verification shows that 7(5) + 3 equals the original right-hand side, 38.

The importance of checking work to ensure the solution is correct.

The process of solving two-step equations involves two main steps: manipulation and verification.

The final solution is x = 5, confirmed by checking.

A summary of the steps to solve two-step equations.

The significance of using inverse operations to isolate the variable.

The method of checking the solution by substituting back into the original equation.

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