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Steps to Solve Multi-Step Equations

Sep 11, 2024

Solving Equations Using Multiple Steps

Introduction

  • Focus on solving equations using multiple steps.
  • Builds on previous knowledge of solving one-step equations.
  • Overview of the steps involved in solving these equations.

Steps to Solve Equations

  1. Clear Fractions or Decimals
    • Use the multiplication principle to eliminate fractions or decimals.
  2. Remove Parentheses
    • Utilize the distributive property to eliminate any parentheses.
  3. Add/Subtract Terms
    • Move all variable terms to one side and all constant terms to the other.
  4. Multiply/Divide to Solve for Variable
    • Isolate the variable by dividing or multiplying as necessary.
  5. Check Solutions
    • Verify the solution by plugging it back into the original equation.

Example Problems

Example 1

  • Original Equation: (3x + 7 = 43)
  • Step 1: No fractions/decimals.
  • Step 2: No parentheses.
  • Step 3: Subtract 7 from both sides: (3x = 36).
  • Step 4: Divide by 3: (x = 12).
  • Check: (3 \times 12 + 7 = 43) checks out.

Example 2

  • Original Equation: (4 - 2x = 10)
  • Step 1 & 2: No fractions/decimals or parentheses.
  • Step 3: Subtract 4 from both sides: (-2x = 6).
  • Step 4: Divide by -2: (x = -3).

Example 3

  • Original Equation: (x/4 + 9 = -5)
  • Step 1: Multiply every term by 4 to clear fraction.
  • Result: (-x - 36 = -20).
  • Step 3: Add 36 to both sides: (-x = 16).
  • Step 4: Divide by -1: (x = -16).

Example 4

  • Original Equation: (4.3 = 1.5x - 5)
  • Step 1: Multiply by 10 to clear decimals.
  • Result: (43 = 15x - 50).
  • Step 3: Add 50: (93 = 15x).
  • Step 4: Divide by 15: (x = 6.2).

Example 5

  • Combine like terms before solving.
  • Example: (8x - 10x + 7 = 10 + 12 + 3x).
  • Simplified: (-2x + 7 = 22 + 3x).
  • Move variable terms to one side: (7 = 22 + 5x).
  • Solve: (x = -3).

Example 6

  • Clear fractions by multiplying.
  • Original: (\frac{2}{3}(6x + 1) = 6).
  • Multiply by 3: (2(6x + 1) = 18).
  • Simplified: (12x + 2 = 18).
  • Solve: (x = \frac{4}{3}).

Checking Solutions with a Graphing Calculator

  • Assign values to X using the calculator.
  • Verify the equation by checking if the left side equals the right side.
  • Examples demonstrated with X = 12 and X = -3.

Conclusion

  • Remember to verify solutions after solving.
  • Use graphing calculators for efficient checking of solutions.

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