5.2 Algebraic Solutions and Interval Notation

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Solved Examples

  1. LCM: The LCM of 4, 3, 5 is 60. Multiply entire inequality by 60. 60(x4)<60(5x−23−7x−35)60 \left( \frac{x}{4} \right) < 60 \left( \frac{5x-2}{3} - \frac{7x-3}{5} \right)
  2. Simplify: 15x<20(5x−2)−12(7x−3)15x < 20(5x - 2) - 12(7x - 3)
  3. Expand: 15x<100x−40−84x+3615x < 100x - 40 - 84x + 36 15x<16x−415x < 16x - 4
  4. Rearrange: 15x−16x<−415x - 16x < -4 −x<−4-x < -4
  5. Multiply by -1 (REVERSE SIGN): x>4x > 4
  6. Solution: (4,∞)(4, \infty).

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