Solving Two-Step Equations | Algebra Equations

Math with Mr. J
5 May 202009:12

Summary

TLDRIn the 'Math with Mr. J' video, the focus is on solving two-step equations. Mr. J demonstrates how to isolate variables by reversing operations, ensuring equation balance. Examples include undoing subtraction and division to isolate 'x' in '2x - 6 = 10', leading to x = 8, and 'R/5 + 8 = 11', resulting in R = 15. The video also covers handling parentheses and variables on different sides of the equation, emphasizing the importance of checking solutions in the original equations.

Takeaways

  • 🔢 The main goal in solving equations is to isolate the variable.
  • ⚖️ To maintain balance, whatever operation is done to one side of the equation must be done to the other side.
  • 🔄 The process involves reversing the order of operations to isolate the variable.
  • ➕ To eliminate subtraction on one side, add the opposite on both sides.
  • ➗ To remove multiplication, use division as the opposite operation.
  • 🔄 For equations like '2x - 6 = 10', first add 6 to both sides to eliminate the subtraction, then divide by 2 to solve for x.
  • 🔄 In equations with division and addition, such as 'r/5 + 8 = 11', subtract 8 from both sides first, then multiply by 5 to solve for r.
  • 🔄 When the variable is on the right side, like in '7 = 16 - 3e', subtract the constant from both sides to move the variable to the left.
  • 🔄 Parentheses can be handled by dividing both sides by the coefficient outside the parentheses to simplify the equation.
  • 🔄 Always check the solution by plugging the isolated variable back into the original equation to ensure accuracy.

Q & A

  • What is the main goal when solving equations with variables?

    -The main goal is to isolate the variable, getting it by itself to solve the equation.

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

    -It is important to perform the same operation on both sides to keep the equation balanced.

  • In the first example, what is the first step to isolate the variable 'x'?

    -The first step is to add 6 to both sides of the equation to eliminate the subtraction of 6 on the left side.

  • How does adding 6 to both sides of the equation 2x - 6 = 10 help in solving for x?

    -Adding 6 to both sides results in 2x = 16, which simplifies the equation and brings us closer to isolating x.

  • What is the reverse operation of multiplication used in the script?

    -The reverse operation of multiplication is division, which is used to isolate the variable by making the coefficient equal to 1.

  • For the equation R / 5 + 8 = 11, how do you reverse the operation of addition?

    -To reverse the addition, you subtract 8 from both sides of the equation to isolate the term with the variable R.

  • What is the purpose of multiplying both sides of an equation by 5 when solving for R in the equation R / 5 + 8 = 11?

    -Multiplying both sides by 5 reverses the division by 5, which helps to isolate the variable R.

  • In the equation 7 = 16 - 3e, how do you handle the negative sign in front of the variable?

    -You divide both sides by -3 to isolate the variable e, reversing the multiplication by -3.

  • Why is it necessary to divide both sides by 2 in the equation 2(y - 8) = 24?

    -Dividing both sides by 2 undoes the multiplication by 2 outside the parentheses, simplifying the equation to y - 8 = 12.

  • How does adding 8 to both sides of the equation y - 8 = 12 help in isolating y?

    -Adding 8 to both sides cancels out the -8 on the left side, leaving y by itself on the left side of the equation.

  • What is the final step to verify the solution to an equation?

    -The final step is to plug the solution back into the original equation to see if it satisfies the equation and yields the correct result.

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