Math Antics: Solving Two-Step Equations

Introduction

• Focus on solving equations with two math operations: addition/subtraction and multiplication/division.
• Builds on previous lessons about single-operation equations.

Two-Step Equations

• Require two steps to solve since they have two arithmetic operations.
• Need to ‘undo’ the operations to isolate the unknown variable (e.g., x).
• Two complications:
  1. More combinations of operations.
  2. Deciding the order to undo operations.

Order of Operations

• Solving equations requires using the Order of Operations in reverse.
• Standard Order of Operations:
  • Parentheses/Groups
  • Exponents
  • Multiplication/Division
  • Addition/Subtraction
• For undoing operations: reverse the order.
  • Undo Addition/Subtraction before Multiplication/Division.

Example 1: Solving 2x + 2 = 8

• Equation involves addition and multiplication.
• Steps:
  1. Undo addition: Subtract 2 from both sides.
  2. Undo multiplication: Divide by 2 on both sides.
• Result: x = 3.

Example 2: Solving x/2 - 1 = 4

• Equation involves division and subtraction.
• Steps:
  1. Undo subtraction: Add 1 to both sides.
  2. Undo division: Multiply by 2 on both sides.
• Result: x = 10.

Importance of Grouping

• Parentheses or brackets group terms, influencing the order of operations.
• Operations inside groups are done first, undone last.

Example 3: Grouped Expression (2(x + 2) = 8)

• Steps:
  1. Undo multiplication: Divide by 2 on both sides.
  2. Undo addition within group: Subtract 2 from both sides.
• Result: x = 2.

Implied Groups within Fractions

• Fraction lines imply grouping of terms above or below them.
• Example: Solving (x - 1)/2 = 4
  • Treat ‘x - 1’ as a group due to fraction line.
  • Steps:
    1. Undo division by 2: Multiply by 2 on both sides.
    2. Undo subtraction within group: Add 1 to both sides.
• Result: x = 9.

Conclusion

• Two-step equations involve multiple operations and groupings.
• Key strategy: Use reverse Order of Operations.
• Pay attention to grouping, including implied groups in fractions.
• Practice with varied problems to master solving two-step equations.
• Visit Math Antics for more learning.