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TALLER 1 DESIGUALDADES Magister. Manuel Antonio Montero Gaona

Resolver las siguientes desigualdades 1) 4 + 9x > –2 + 7x 2) 5 – 3x < 13 + 3x

5) 1-x≤2

6) 8-3x≤2x-15-2x≥38) + 4 ≤

3

5−2 3

+1

9.

Write the following sets of numbers in the interval form : (a) (c) {x | –2 ≤ x ≤ 7} {t | t < 4} (b) {x | –2 < x ≤ 5} (d) {y | y ≥ –3}10. 11. 12. 13. 14. 15. 16. 17. 18.

x  2 2  3x x 1 1 2x    4 2 3 Solve : 3
Solve :

x  2 x  1 3x  2 x  1    3 2 4 3

Answer : Answer : Answer :

x ≤–16/7

Solve : (2x – 3)(3x + 1) > (3x + 2)(2x – 5) Solve : (2x – 1)(3x + 2) < (x + 1)(6x – 5) Solve : 3x – 4 < x – 2< 2x + 1 Solve : 1 – 3x ≥ 2x + 11 ≥ x + 9 Solve : (x + 3)2 >(x – 2)2 Solve : – 5 ≤ 3 – 2x ≤ 5 Answer :

x > –7/4 no solution

Answer : Answer : Answer : –1 ≤ x ≤ 4

–3 < x < 1 x =–2 x > –1/2

Solve : x – 3 ≤ 3 – 2x ≤ 1 – x (x +3)2 > (x – 2)2

Answer :

x = 2 only

19. A man has $5,000 to invest. He wants to invest some of it at 8% and the rest at 10%. What is the maximum amount he should invest at8% if he wants an annual interest income of atleast $ 460 ? Answer : $2,000. 20. Sylvia has $10,000, which she wants to invest, some at 6% and the rest at 9%. If she wants anannual interest income of atleast $ 720, what is the minimum amount she should invest at 9% ? Answer : $4,000 21. 22. 33. 24 25 26 27. Solve: 19 + (3x + 5)(2x –1) ≤ (5x + 3)(x +2) Solve : (2x + 1)(x + 3) < (x + 10)(x – 3) Solve : (3x + 2)(x + 1) > (2x + 5)(x – 3) Solve : 18 + (2x + 1)(x – 2) ≤ 4(x – 1)2 Solve : x2 + 6x + 15 ≤ 0 Solve : x2 + 6x + 9 > 0Solve : 4x2 – 4x + 1 ≤ 0 Answer : Answer : Answer : Answer : Answer : Answer : Answer : 2 ≤ x ≤ 4. no solution. all x. x ≤ –3/2 or x ≥ 4 no solution. all x ≠ –3. x = 1/2