Learn on PengiPengi Math (Grade 8)Chapter 3: Solving Linear Equations

Lesson 2: Solving Equations with Variables on Both Sides

In this Grade 8 Pengi Math lesson from Chapter 3, students learn to solve linear equations with variables on both sides by applying a four-step strategy: simplify, collect variables, collect constants, and isolate. The lesson covers using inverse operations to group like terms, correctly handling negative coefficients, and distributing negative signs into parentheses. Students also practice verifying their solutions by substituting values back into the original equation.

Section 1

Solving Equations with Variables on Both Sides

Property

Step 1. Simplify each side of the equation as much as possible.

  • Use the Distributive Property to remove any parentheses.
  • Combine like terms.

Step 2. Collect all the variable terms on one side of the equation.

  • Use the Addition or Subtraction Property of Equality.

Step 3. Collect all the constant terms on the other side of the equation.

  • Use the Addition or Subtraction Property of Equality.

Step 4. Make the coefficient of the variable term to equal to 1.

  • Use the Multiplication or Division Property of Equality.
  • State the solution to the equation.

Step 5. Check the solution.

  • Substitute the solution into the original equation to make sure the result is a true statement.

Examples

Section 2

Working with Negative Coefficients

Property

When a negative sign is in front of a parenthesis, it must be distributed to every term inside, changing the sign of each term.

−(a+b)=−a−b-(a + b) = -a - b
−(a−b)=−a+b-(a - b) = -a + b

Examples

Book overview

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Chapter 3: Solving Linear Equations

  1. Lesson 1

    Lesson 1: Simplifying and Solving One-Step & Multi-Step Equations

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  2. Lesson 2Current

    Lesson 2: Solving Equations with Variables on Both Sides

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  3. Lesson 3

    Lesson 3: Equations with Rational Coefficients (Fractions and Decimals)

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  4. Lesson 4

    Lesson 4: Analyzing Number of Solutions (One, None, Infinite)

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  5. Lesson 5

    Lesson 5: Literal Equations and Real-World Applications

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Lesson overview

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Section 1

Solving Equations with Variables on Both Sides

Property

Step 1. Simplify each side of the equation as much as possible.

  • Use the Distributive Property to remove any parentheses.
  • Combine like terms.

Step 2. Collect all the variable terms on one side of the equation.

  • Use the Addition or Subtraction Property of Equality.

Step 3. Collect all the constant terms on the other side of the equation.

  • Use the Addition or Subtraction Property of Equality.

Step 4. Make the coefficient of the variable term to equal to 1.

  • Use the Multiplication or Division Property of Equality.
  • State the solution to the equation.

Step 5. Check the solution.

  • Substitute the solution into the original equation to make sure the result is a true statement.

Examples

Section 2

Working with Negative Coefficients

Property

When a negative sign is in front of a parenthesis, it must be distributed to every term inside, changing the sign of each term.

−(a+b)=−a−b-(a + b) = -a - b
−(a−b)=−a+b-(a - b) = -a + b

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 3: Solving Linear Equations

  1. Lesson 1

    Lesson 1: Simplifying and Solving One-Step & Multi-Step Equations

    LearnPractice
  2. Lesson 2Current

    Lesson 2: Solving Equations with Variables on Both Sides

    LearnPractice
  3. Lesson 3

    Lesson 3: Equations with Rational Coefficients (Fractions and Decimals)

    LearnPractice
  4. Lesson 4

    Lesson 4: Analyzing Number of Solutions (One, None, Infinite)

    LearnPractice
  5. Lesson 5

    Lesson 5: Literal Equations and Real-World Applications

    LearnPractice