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Lecture Notes on Exercise 2.1

Jul 28, 2024

Lecture Notes on Exercise 2.1

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Overview of Exercise 2.1

  • Focuses on solving equations and checking results.
  • Need to ensure LHS equals RHS for verification.

Key Concepts

  • Like Terms: Combine terms with the same variables.
  • Checking Results: Substitute the value back into the original equation to ensure both sides are equal.

Example Solutions

Question 1: Solve 3x = 2x + 18

  1. Move 2x to LHS: 3x - 2x = 18
  2. Simplify to find x: 1x = 18
  3. Result: x = 18
  4. Check: Substitute in original equation, verify LHS = RHS.

Question 2: Solve 5t - 3 = 3t - 5

  1. Move 3t to LHS: 5t - 3t = -5 + 3
  2. Simplify: 2t = -2
  3. Result: t = -1
  4. Check: Substitute value in original equation.

Question 3: Solve 5x + 9 = 5 + 3x

  1. Move 3x to LHS: 5x - 3x = 5 - 9
  2. Simplify: 2x = -4; Therefore, x = -2
  3. Check: Substitute in equation.

Question 4: Solve 4z + 3 = 6 + 2z

  1. Move 2z to LHS: 4z - 2z = 6 - 3
  2. Simplify: 2z = 3; Therefore, z = 3/2
  3. Check: Substitute value in original equation.

Question 5: Solve 2x - 1 = 14 - x

  1. Move -x to LHS: 2x + x = 14 + 1
  2. Simplify: 3x = 15; Therefore, x = 5
  3. Check: Substitute value.

Question 6: Solve 8x + 4 = 3(x - 1) + 7

  1. Expand the bracket: 8x + 4 = 3x - 3 + 7
  2. Combine like terms: 8x = 3x + 4
  3. Solve: 5x = 4; Therefore, x = 4/5
  4. Check: Substitute value in equation.

Question 7: Solve x = 4/5(x + 10)

  1. Expand: x = 4/5x + 8
  2. Combine like terms to find x: x - 4/5x = 8
  3. Result: x = 40
  4. Check: Substitute back.

Question 8: Solve 2x/3 + 1 = 7x/15 + 3

  1. Move like terms: 2x/3 - 7x/15 = 3 - 1
  2. Solve to find x: Result: x = 10
  3. Check: Substitute back into original equation.

Question 9: Solve 2y + 5/3 = 26/3 - y

  1. Move like terms: 2y + y = 26/3 - 5/3
  2. Simplify to find y: Result: y = 7/3
  3. Check: Substitute value.

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