Routine Other Solving Practice #3
Solve:
1. 9(3 + x) > –11
2. 4 – 9x < –8
3. 8x – 5 < –6
4. 12x – 3 > 7x + 11
5. 59 – 3x < 11
6. 2x – 6 > 8
7. 9(x + 3) < –9
8. 6 – 5x > 3
9. 6x – 11 > 14x
10. 1 – 8x < 10
11. (x – 7)(x + 5) = 0
12. x² + 21x + 108 = 0
13. x² + 8x + 7 = 0
14. x² – 13x + 12 = 0
15. (x + 5)(x + 6) = 0
16. x² + 8x + 15 = 0
17. x² = 8x – 15
18. x² = 10x – 16
19. x² + 5x – 24 = 0
20. x² + x = 30
Answers: Routine Other Solving Practice #3
Solve:
1. 9(3 + x) > –11 27 + 9x > –11 9x > –11 – 27 x > –4.222 or –37/9
2. 4 – 9x < –8 4 < –8 + 9x 4 + 8 < 9x x > 1.333 or 4/3
3. 8x – 5 < –6 8x < –6 + 5 x < –1 ÷ 8 x < –0.125 or –1/8
4. 12x – 3 > 7x + 11 12x – 7x – 3 > 11 5x > 11 + 3 x > 2.8 or 14/5
5. 59 – 3x < 11 59 < 11 + 3x 59 – 11 < 3x x < 16
6. 2x – 6 > 8 2x > 8 + 6 x > 14 ÷ 2 x>7
7. 9(x + 3) < –9 9x + 27 < –9 9x < –9 – 27 x < –4
8. 6 – 5x > 3 6 > 3 + 5x 6 – 3 > 5x x < 0.6 or 3/5
– –
9. 6x – 11 > 14x 11 > 14x – 6x 11 > 8x x < –1.375 or –11/8
10. 1 – 8x < 10 1 < 10 + 8x 1 – 10 < 8x x > –1.125 or –9/8
Note that steps are chosen to always avoid negative multipliers of x.
Some intermediate steps have been left out for reasons of room.
11. (x – 7)(x + 5) = 0 x = 7 or x = –5
12. x² + 21x + 108 = 0 (x + 12)(x + 9) = 0 x = –12 or x = –9
13. x² + 8x + 7 = 0 (x + 7)(x + 1) = 0 x = –1 or x = –7
14. x² – 13x + 12 = 0 (x – 1)(x – 12) = 0 x = 1 or x = 12
15. (x + 5)(x + 6) = 0 x = –5 or x = –6
16. x² + 8x + 15 = 0 (x + 3)(x + 5) = 0 x = –5 or x = –3
17. x² = 8x – 15 x² – 8x + 15 = 0 (x – 3)(x – 5) = 0 x = 3 or x = 5
18. x² = 10x – 16 x² – 10x + 16 = 0 (x – 8)(x – 2) = 0 x = 8 or x = 2
19. x² + 5x – 24 = 0 (x – 3)(x + 8) = 0 x = –8 or x = 3
20. x² + x = 30 x² + x – 30 = 0 (x – 5)(x + 6) = 0 x = –6 or x = 5
Quadratic solutions must have both answers.
