Solving Two-Step Equations

Topics Covered

• Basic two-step equations
• Equations with fractions
• Equations with parentheses
• Variables on both sides
• Equations with decimals

Basic Two-Step Equations

1. Example: Solve (3x + 5 = 17)

   • Isolate (x) by subtracting 5 from both sides: (3x = 12)
   • Divide by 3: (x = 4)

2. Example: Solve (4x + 3 = 19)

   • Subtract 3: (4x = 16)
   • Divide by 4: (x = 4)

Equations with Negative Coefficients

1. Example: (17 - 5x = 2)
   • Subtract 17: (-5x = -15)
   • Divide by -5: (x = 3)

Equations with Fractions

1. Example: (9 = 3 + \frac{x}{4})

   • Subtract 3: (6 = \frac{x}{4})
   • Multiply by 4: (x = 24)

2. Example: (8 + \frac{x}{3} = 12)

   • Subtract 8: (\frac{x}{3} = 4)
   • Multiply by 3: (x = 12)

Variables on Both Sides

1. Example: (3x + 8 + 5x = 32)

   • Combine like terms: (8x + 8 = 32)
   • Subtract 8: (8x = 24)
   • Divide by 8: (x = 3)

2. Example: (7x + 2 - 3x = 26)

   • Combine like terms: (4x + 2 = 26)
   • Subtract 2: (4x = 24)
   • Divide by 4: (x = 6)

Multi-Step Equations

1. Example: (13 - 2x = 4x)
   • Add 2x to both sides: (13 = 6x)
   • Divide by 6: (x = \frac{13}{6})

Equations with Parentheses

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

Equations with Decimals

1. Example: (0.2x + 0.3 = 1.5)
   • Multiply every term by 10 to eliminate decimals
   • Solve like a regular equation after clearing decimals

Algebra Course Topics on Udemy

• Basic arithmetic
• Fractions
• Linear equations
• Order of operations
• Graphing linear equations
• Inequalities and absolute value
• Polynomials and factoring
• Systems of equations
• Quadratic equations
• Rational and radical expressions
• Complex numbers
• Exponential functions and logarithms
• Functions and graphing
• Conic sections
• Sequences and series

Exploration of these topics includes quizzes and further examples, beneficial for a deeper understanding of algebra concepts.