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Techniques for Solving Multi-Step Equations

May 23, 2025

Math with Mr. J: Solving Multi-Step Equations

Overview

  • This lecture covers methods to solve multi-step equations.
  • Techniques discussed include the distributive property, combining like terms, and handling variables on both sides of an equation.
  • Two examples are provided to illustrate these methods.

General Steps for Solving Multi-Step Equations

  1. Distributive Property: Remove parentheses by distributing any coefficients outside parentheses.
  2. Combine Like Terms: Look for and combine like terms on each side of the equation.
  3. Variables on Both Sides: If variables appear on both sides, move them to one side.
  4. Isolate the Variable: Use inverse operations (addition/subtraction, multiplication/division) in reverse order of operations to solve for the variable.
  5. Check Solution: Substitute the solution back into the original equation to verify.

Example 1

Equation: x + 5(3x - 4) = 12x + 4

  • Distributive Property:
    • Distribute 5: 5 * 3x = 15x and 5 * -4 = -20
    • Equation becomes: x + 15x - 20 = 12x + 4
  • Combine Like Terms:
    • Combine x and 15x: Result is 16x
    • New equation: 16x - 20 = 12x + 4
  • Variables on Both Sides:
    • Subtract 12x from both sides to get 4x - 20 = 4
  • Isolate the Variable:
    • Add 20 to both sides: 4x = 24
    • Divide by 4: x = 6
  • Check Solution:
    • Substitute x = 6 into the original equation, both sides equal 76, confirming the solution.

Example 2

Equation: -9(m - 2) + 7m = -10

  • Distributive Property:
    • Distribute -9: -9 * m = -9m and -9 * -2 = 18
    • Equation becomes: -9m + 18 + 7m = -10
  • Combine Like Terms:
    • Combine -9m and 7m: Result is -2m
    • New equation: -2m + 18 = -10
  • Isolate the Variable:
    • Subtract 18 from both sides: -2m = -28
    • Divide by -2: m = 14
  • Check Solution:
    • Substitute m = 14 into the original equation, the equation checks out.

Conclusion

  • The video provides clear steps to solve multi-step equations using common algebraic techniques.
  • Both examples emphasize checking the solution by substitution to ensure accuracy.

Helpful Tips

  • Always perform operations on both sides of the equation to maintain balance.
  • Use inverse operations in reverse order of operations to efficiently isolate the variable.
  • Double-check work by substituting the solution back into the original equation.

Full transcript