Inequalities.pdf

Desigualdades
1. Resolva as seguintes desigualdades.
(a) 2x − 3 < 5x + 7.
x > −10/2
(b) 3 − 7x ≥ 9x + 1.
x ≤ 1/4
(c) 5x + 17 > 2 − 7x.
x > −5/3
(d) 2x − 3 ≤ 4x − 11.
x ≥ 8/3
(e) 0,6 − 0,2y > 1,2y − 0,1.
y < 7/10
(f) 2/3 − 2x ≥ −1/3 + 4x.
x ≤ −2/5
(g) 5(x − 3) > 2(5 − 2x).
x > 25/9
(h) −2(2x + 4) ≤ 6(3 − 2x).
x ≤ 13/2
(i) 2 − (3z − 5) > −4(9 − 2z).
z < 43/11
(j) 2(x − a) ≥ −3(x + b).
x ≥ (2a − 3b)/5
(k) 2(x − 3a) + 3(x − 4a) > −a − 3(x − b).
x > (17a + 3b)/8
(l) (x − 3)(x − 4) ≤ (6 − x)(7 − x).
x ≤ 5
(m) (2x + 1)(2x − 5) ≥ (4x − 3)(x + 8).
x ≤ 19/2
(n) 3u² − (u − 5)(u − 1) < (u − 10)(2u + 3).
u < −25/23
(o) x² + 1 > x³.
x < 7
(p) 5x¹ − 3x² ≥ 5x.
x ≤ −1/3
(q) x² > 7x.
x < 2/5
(r) 3r⁵ ≤ r².
r ≤ 5/16
(s) x⁻² > 4x.
x < 0
(t) 3x + x² ≥ x + 1.
x ≥ 17/23
(u) x³ + 4x⁻¹ > 3x + 2x⁻⁵.
x < −1/19
(v) x⁰,⁵ + 0,3(x − 1) ≤ x⁻⁴.
x ≤ 109/79
(w) 0,1(2x − 1) − 0,2(3 − x) > x.
x > −43/9
(x) x⁴ − x³ ≥ 3.
x ≥ 36/31
(y) x⁻¹ − 3x⁻³ ≤ x + 2.
x ≥ −1/6
(z) 3 − x⁻² + 1 > x.
x < 37/7
2. Resolva as seguintes desigualdades triplas.
(a) 11 < 2x + 5 < 27.
3 < x < 11
(b) −11 < 3x + 1 ≤ 100.
−4 < x ≤ 33
(c) 2x − 1 ≤ 3x < 2x + 3.
−1 ≤ x < 3
(d) 4 + y ≤ 3y + 7 ≤ 2y + 15.
−3/2 ≤ y ≤ 8
(e) 5 ≤ x − 6 < 7x + 8.
x ≥ 11
(f) 2x + 7 ≤ 8 ≤ 15x + 2.
2/5 ≤ x ≤ 1/2
(g) x² ≤ x³ ≤ 8x.
17/23 ≤ x ≤ 1
(h) 2x − 3 + 5 < x³ − 1 < x².
x > 163/13
(i) x³ − 2x ≤ 2x + 3 < 5.
sem soluções
(j) 1 − x ≤ 2x + 1 < x + 3.
1/9 < x < 1
(k) 5 + x + x + 4 < 3 − x ≤ x + x.
sem soluções
(l) 5 − x < x³ + x < 3 − x + 5x.
x > 3
(m) 2(x − 5) − x + 1 ≤ 4x − 1 < x².
−4/5 < x ≤ 43/15
2.