Algebra 1 Final Exam Review - Key Concepts and Problem Solving

Overview

• Focus on 33 different question types totaling 80 problems.
• Emphasis on problem-solving strategies and understanding algebraic concepts.
• Encouragement to pause and attempt problems independently.
• Additional resources available on Mario's Math Tutoring YouTube channel.

Problem 1: Solving Equations

• Equation: (-3(x - 2) - 5 = -11)
• Steps to solve:
  1. Distribute (-3) into the parentheses: (-3x + 6).
  2. Simplify by combining like terms: (6 - 5 = 1).
  3. Rearrange to isolate the variable (subtract 1 from both sides): (-3x = -12).
  4. Solve for (x) by dividing both sides by (-3): (x = 4).
• Concepts tested:
  • Understanding the distributive property.
  • Ability to solve linear equations.

Problem 2: Solving Proportions

• Equation: (\frac{5x - 2}{20} = \frac{x}{5})
• Steps to solve:
  1. Use the cross-multiplying technique:
     • ((5x - 2) \times 5 = 20 \times x).
  2. Distribute the 5: (25x - 10).
  3. Get variables on one side, numbers on the other:
     • Subtract (25x) from both sides: (20 - 25x = -5x).
  4. Solve for (x) by dividing by (-5): (-10 / -5 = 2).
• Concepts tested:
  • Understanding of proportions (ratios equal to ratios).
  • Application of the cross-multiplication method.

Additional Notes

• Verification by substituting the solution back into the original problem.
• Encouragement to ensure both sides of the equation are equal as a check for correctness.