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Solving Two-Step Equations

May 26, 2024

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Solving Two-Step Equations Lecture

Table of Contents

  • Basic Two-Step Equations
  • Two-Step Equations with Fractions, Parentheses, Decimals
  • Multi-Step Equations
  • Special Cases
  • Course Recommendations

Basic Two-Step Equations

  • 3x + 5 = 17

    • Subtract 5 from both sides: 3x = 12
    • Divide both sides by 3: x = 4

  • 4x + 3 = 19

    • Subtract 3 from both sides: 4x = 16
    • Divide both sides by 4: x = 4

  • 17 - 5x = 2

    • Subtract 17 from both sides: -5x = -15
    • Divide both sides by -5: x = 3

Two-Step Equations with Fractions

  • 9 = 3 + x / 4

    • Subtract 3 from both sides: 6 = x / 4
    • Multiply both sides by 4: x = 24

  • 8 + x / 3 = 12

    • Subtract 8 from both sides: x / 3 = 4
    • Multiply both sides by 3: x = 12

Equations with Variables on Both Sides

  • 7x + 2 - 3x = 26
    • Combine like terms: 4x + 2 = 26
    • Subtract 2 from both sides: 4x = 24
    • Divide both sides by 4: x = 6

Multi-Step Equations with Multiple Variables

  • 3x + 8 + 5x = 32

    • Combine like terms: 8x + 8 = 32
    • Subtract 8 from both sides: 8x = 24
    • Divide both sides by 8: x = 3

  • 7x + 2 - 3x = 26

    • Combine like terms: 4x + 2 = 26
    • Subtract 2 from both sides: 4x = 24
    • Divide by 4: x = 6

Equations with Distribution

  • 3 * (2x - 4) + 1 = 7
    • Distribute: 6x - 12 + 1 = 7
    • Combine like terms: 6x - 11 = 7
    • Add 11 to both sides: 6x = 18
    • Divide by 6: x = 3*

Equations with Multiple Fractions

  • 2x/3 + 4 = 3x/2 - 1
    • Find the least common multiple (6) and multiply all terms: 4x + 24 = 9x - 6
    • Move all x terms to one side: 9x - 4x = 24 + 6
    • Simplify: 5x = 30
    • Divide by 5: x = 6

Equations with Decimals

  • 2x + 0.3 = 1.5
    • Convert to whole numbers by multiplying by 10: 20x + 3 = 15
    • Subtract 3 from both sides: 20x = 12
    • Divide by 20: x = 0.6

Course Recommendations

  • Udemy Algebra Course
    • Basic Arithmetic
    • Fractions
    • Solving Linear Equations
    • Order of Operations
    • Graphing Linear Equations
    • Inequalities and Absolute Value
    • Polynomials and Factoring
    • Systems of Equations
    • Quadratic Equations
    • Rational and Radical Expressions
    • Exponential Functions and Logarithms
    • Functions and Conic Sections
    • Sequences and Series

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