Solving Linear Equations with Variables on Both Sides

Algebra 1 Grades High School 4:07 Video
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Lesson Description

Learn how to solve linear equations where variables appear on both sides of the equals sign. This lesson covers isolating the variable by using inverse operations and simplifying expressions.

Video Resource

Example 2: Variables on both sides | Linear equations | Algebra I | Khan Academy

Khan Academy

Duration: 4:07
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Key Concepts

  • Inverse Operations
  • Combining Like Terms
  • Properties of Equality

Learning Objectives

  • Students will be able to isolate variables in linear equations with variables on both sides.
  • Students will be able to apply the properties of equality to manipulate equations and find solutions.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic principles of solving linear equations, emphasizing the importance of maintaining balance by performing the same operation on both sides of the equation. Briefly recap inverse operations (addition/subtraction, multiplication/division).
  • Video Presentation (10 mins)
    Play the Khan Academy video "Example 2: Variables on both sides | Linear equations | Algebra I | Khan Academy". Encourage students to take notes on the steps demonstrated in the video.
  • Guided Practice (15 mins)
    Work through a similar example problem on the board, explaining each step clearly. Involve students by asking them what operation should be performed next and why. Example: 5x + 3 = 2x - 9
  • Independent Practice (15 mins)
    Assign students a set of practice problems to solve independently. Circulate the room to provide assistance and answer questions. Example problems: 8y - 5 = 3y + 10; -4a + 7 = 2a - 5; 12 - 2z = 4z + 6
  • Review and Wrap-up (5 mins)
    Review the solutions to the practice problems. Address any remaining questions or misconceptions. Summarize the key steps for solving linear equations with variables on both sides.

Interactive Exercises

  • Equation Balance
    Use a virtual balance scale to demonstrate how performing the same operation on both sides keeps the equation balanced. (Many free online resources available.)
  • Group Problem Solving
    Divide students into small groups and assign each group a challenging equation to solve. Have them present their solution to the class, explaining their reasoning.

Discussion Questions

  • Why is it important to perform the same operation on both sides of an equation?
  • What are some strategies for deciding which variable term to eliminate first?

Skills Developed

  • Problem-solving
  • Algebraic manipulation
  • Logical reasoning

Multiple Choice Questions

Question 1:

What is the first step in solving the equation 3x + 5 = x - 1?

Correct Answer: Subtract x from both sides

Question 2:

When solving an equation, what must you always do to maintain balance?

Correct Answer: Perform the same operation on both sides

Question 3:

Solve for x: 2x - 4 = x + 3

Correct Answer: x = 7

Question 4:

What is the inverse operation of addition?

Correct Answer: Subtraction

Question 5:

Solve for y: 5y + 2 = 3y - 6

Correct Answer: y = -4

Question 6:

What is the goal when solving for x in an equation?

Correct Answer: Isolate x on one side of the equation

Question 7:

Solve for a: -2a + 8 = 4a - 4

Correct Answer: a = 2

Question 8:

Which operation would you use to isolate x in the equation 5x = 20?

Correct Answer: Division

Question 9:

Solve for z: 6z - 10 = 2z + 6

Correct Answer: z = 4

Question 10:

What is a constant term in an equation?

Correct Answer: A term without a variable

Fill in the Blank Questions

Question 1:

The opposite of adding is _________.

Correct Answer: subtracting

Question 2:

To solve for a variable, you must _________ it.

Correct Answer: isolate

Question 3:

The opposite of multiplying is _________.

Correct Answer: dividing

Question 4:

Solve for x: 4x + 2 = 2x + 8. x = _________

Correct Answer: 3

Question 5:

When solving an equation, whatever you do to one side, you must also do to the _________ side.

Correct Answer: other

Question 6:

Solve for y: 7y - 5 = 3y + 7. y = _________

Correct Answer: 3

Question 7:

Terms that have the same variable raised to the same power are called _________ terms.

Correct Answer: like

Question 8:

Solve for a: -3a + 10 = 5a - 6. a = _________

Correct Answer: 2

Question 9:

Operations that undo each other are called _________ operations.

Correct Answer: inverse

Question 10:

Solve for z: 9z - 12 = 5z + 4. z = _________

Correct Answer: 4

Educational Standards

A1.A.1:Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context. A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties.

Teaching Materials

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