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Mastering Multi-Step Inequalities Solutions

Learn to solve complex inequalities involving fractions, distribution, combination of terms, and variable manipulation. Understand how to get the variable on the left side, flip inequalities, and ensure accurate solutions.

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Mastering Multi-Step Inequalities Solutions

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  1. You Will Be Able To: Solve Multi-step Inequalities

  2. Fraction bust Distribute Combine like terms on each side Get variable on one side (left if possible) Undo If by negative, flip inequality Make sure variable is on the left

  3. -4 -4 2x 2 2 2 x 1 -1 0 1

  4. +1 +1 3p 6 3 3 p 2 -2 0 2

  5. +1 +1 -4c 4 -4-4 c -1 -1 0 1

  6. 3p – 6 6 +6 +6 3p 12 3 3 p 4 -4 0 4

  7. -4d -4d 6d – 9 15 +9 +9 24 6d 66 d 4 -4 0 4

  8. All Real #s When the final solution is true 2x + 3 > 2x – 4 3 > –4 No Solution When the final solution is not true 2x + 5 > 2x + 7 5 > 7

  9. 4y + 1 4y – 8 -4y -4y 1 –8

  10. 5x –8 5x –4 -5x -5x –4 –8

  11. 3b – 3 3b + 3 -3b -3b 3 –3

  12. -5x -5x x + 2 2 -2 -2 x 0

  13. 3a + 1 1 + 3a -3a -3a 1 1

  14. 4n – 40 –36 +40 +40 4 4n 4 4 n 1 -1 0 1

  15. 3( ) n + 2 –21 3n + 6 –21 -6 -6 -27 3n 3 3 n -9 -9 0 9

  16. 8x – 2x 3x + 36 6x 3x + 36 -3x -3x 36 3x 3 3 x 12 -12 0 12

  17. 2c – 60 0

  18. 2c – 60 0 +60 +60 60 2c 2 2 c 30

  19. 320 80p – 320 0

  20. 80p – 320 0 +320 +320 320 80p 80 80 p 4

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