Solve each inequality

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2.1 EXERCISES Solve each inequality. 2. 4x-8 > 2+ 3x 3. 7x-3 > 6x-2 1. 3n-9 > 2n-8 1 1 53 y + – — 12 4 5. 6. 8x – 72 7x-2 2 3 4. d + 3 2x + 7 10. 6x -+ 25x -5 11. – 8 4 18 6 13. 2x-2 3(2x – 5) 19. 2(2-5) 3(5-2y) 20. 3(2x-5) 8x-5 21. 2(3x – 1) > 3x+4 22. 3(x – 2)2-5(x-2) 23. *;** (2x+6) 3 25. 48+ x 2 5(2x + 4) – 2x 26. 24 2 6x-2(3x – 5)+2x 27. 3(x – 8) < 3x-1=”” 29.=”” -2(x+7)=”” 3(x+2)=”” 30.=”” 3(x-5)=””>-(x+3) 31. 15x+354 32. 1<>< 12=”” or=”” x=”” +7=””>10 38. x+4 -12 39. – 2xs-4 or 5x – 20 25 40. Si or xs-3 41. Os 2x-359 42. -552(x+4)58 43. -6<=2x-1_2 45.=”” os=”” 5-2x=”” 5=”” give=”” call=”” neg=”” the=”” .4s2x+3=”” si=”” 47.=”” ssx+15-2=”” !=”” 1=”” win=””> 2+ 3x 3. 7x-3 > 6x-2 1. 3n-9 > 2n-8 1 1 53 y + – — 12 4 5. 6. 8x – 72 7x-2 2″ style=&#39;width:332.4pt;height:249pt;rotation:90;visibility:visible; mso-wrap-style:square&#39;> 2+ 3x 3. 7x-3 > 6x-2 1. 3n-9 > 2n-8 1 1 53 y + – — 12 4 5. 6″>

The Correct Answer and Explanation is :

Let’s solve each of the given inequalities step by step:

1. Solve: 3n – 9 > 2n – 8

  • Subtract 2n from both sides: 3n – 2n – 9 > 2n – 2n – 8, simplifying to n – 9 > -8.
  • Add 9 to both sides: n – 9 + 9 > -8 + 9, simplifying to n > 1.

2. Solve: 4x – 8 > 2 + 3x

  • Subtract 3x from both sides: 4x – 3x – 8 > 2 + 3x – 3x, simplifying to x – 8 > 2.
  • Add 8 to both sides: x – 8 + 8 > 2 + 8, simplifying to x > 10.

3. Solve: 7x – 3 > 6x – 2

  • Subtract 6x from both sides: 7x – 6x – 3 > 6x – 6x – 2, simplifying to x – 3 > -2.
  • Add 3 to both sides: x – 3 + 3 > -2 + 3, simplifying to x > 1.

4. Solve: d + 3 < 2x + 7

  • Subtract 3 from both sides: d + 3 – 3 < 2x + 7 – 3, simplifying to d < 2x + 4.

5. Solve: 8x – 7 < 2x + 3

  • Subtract 2x from both sides: 8x – 2x – 7 < 2x – 2x + 3, simplifying to 6x – 7 < 3.
  • Add 7 to both sides: 6x – 7 + 7 < 3 + 7, simplifying to 6x < 10.
  • Divide both sides by 6: 6x / 6 < 10 / 6, simplifying to x < 5/3.

6. Solve: 8x – 7 < 2x + 3

  • Subtract 2x from both sides: 8x – 2x – 7 < 2x – 2x + 3, simplifying to 6x – 7 < 3.
  • Add 7 to both sides: 6x – 7 + 7 < 3 + 7, simplifying to 6x < 10.
  • Divide both sides by 6: 6x / 6 < 10 / 6, simplifying to x < 5/3.

7. Solve: 2x – 2 < 3(2x – 5)

  • Expand the right side: 2x – 2 < 6x – 15.
  • Subtract 2x from both sides: 2x – 2 – 2x < 6x – 15 – 2x, simplifying to -2 < 4x – 15.
  • Add 15 to both sides: -2 + 15 < 4x – 15 + 15, simplifying to 13 < 4x.
  • Divide both sides by 4: 13 / 4 < 4x / 4, simplifying to 13/4 < x.

8. Solve: 2(2 – 5) < 3(5 – 2y)

  • Simplify both sides: 2(-3) < 3(5 – 2y), which simplifies to -6 < 15 – 6y.
  • Subtract 15 from both sides: -6 – 15 < 15 – 15 – 6y, simplifying to -21 < -6y.
  • Divide both sides by -6: -21 / -6 < -6y / -6, simplifying to 7/2 > y.
  • Since we divided by a negative number, the inequality sign flips.

9. Solve: 3(2x – 5) < 8x – 5

  • Expand both sides: 6x – 15 < 8x – 5.
  • Subtract 6x from both sides: 6x – 6x – 15 < 8x – 6x – 5, simplifying to -15 < 2x – 5.
  • Add 5 to both sides: -15 + 5 < 2x – 5 + 5, simplifying to -10 < 2x.
  • Divide both sides by 2: -10 / 2 < 2x / 2, simplifying to -5 < x.

10. Solve: 6x + 25x – 5 < 0

  • Combine like terms: 31x – 5 < 0.
  • Add 5 to both sides: 31x – 5 + 5 < 0 + 5, simplifying to 31x < 5.
  • Divide both sides by 31: 31x / 31 < 5 / 31, simplifying to x < 5/31.

11. Solve: -8 < 4x – 18

  • Add 18 to both sides: -8 + 18 < 4x – 18 + 18, simplifying to 10 < 4x.
  • Divide both sides by 4: 10 / 4 < 4x / 4, simplifying to 5/2 < x.

12. Solve: 2x – 2 < 3(2x – 5)

  • Expand both sides: 2x – 2 < 6x –

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