nerovnice –
cvičné příklady
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7 – x ≤ 10 -x ≤ 3 x ≥ -3 x ϵ ‹-3 ; ∞) |
2y – 10 ≥ -9 2y ≥ 1 y ≥ y ϵ ‹ |
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12 – x ≥ 7 -x ≥ -5 x ≤ 5 x
ϵ (-∞ ; |
7 – 3a < -17 -3a < -24 a > 8 a ϵ (8; ∞) |
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2 – z < 60 -z < 58 z > -58 z ϵ (-58; ∞) |
3(2 – x) – 2(3x – 1) > 36 6 – 3x – 6x + 2 > 36 -9x + 8 > 36 -9x > 28 x < x ϵ (-∞ ; |
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pro
b > 0: 8 + b > 3b 8 > 2b b < 4 b ϵ
(0 ; 4) |
pro
b < 0: 8 + b <
3b 8 <
2b b > 4 b ϵ Ø |
pro
a > 0: 2 < 6a
a > a ϵ ( |
pro
a < 0: 2 > 6a
a < a ϵ (-∞ ; |
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b ϵ (0 ; 4) |
a
ϵ (-∞ ; |
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c – 7 ≥ 7 c ≥ 14 c
ϵ ‹14 ; ∞) |
x ≤ x – 11 0 ≤ -11 x
ϵ Ø |
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x – 2 + x ≥ -7x -2 ≥ -9x
x ≥ x ϵ ‹ |
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pro
(1 – x) >
0, 1 > x: 5 + 2(1 – x) < 3(1 – x) 5 + 2 – 2x < 3 – 3x -2x
+ 3x < 3 – 5 – 2 x < -4 x
ϵ (-∞ ; |
pro
(1 – x) < 0, 1 < x: 5 + 2(1 – x) > 3(1 – x) 5 + 2 – 2x > 3 – 3x -2x
+ 3x > 3 – 5 – 2 x > -4 x
ϵ (1 ; ∞) |
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x
ϵ (-∞ ; |
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3(2x + 1) > 8x 6x + 3 > 8x -2x > -3 x < x
ϵ (-∞ ; |
x + 2 ≤ 15(5 – x) x + 2 ≤ 75 – 15x 16x ≤ 73 x ≤ x
ϵ (-∞ ; |
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2(x – 2) – (2 – x) < 24 2x – 4 – 2 + x < 24 3x – 6 < 24 3x < 30 x < 10 x
ϵ (-∞ ;10) |
4(x – 1) – 3(x + 2) ≤ 24 4x – 4 – 3x – 6 ≤ 24 x – 10 ≤ 24 x ≤ 34 x
ϵ (-∞ ; |
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6 – 3x – 4x – 4 ≤ 24 2 – 7x ≤ 24 -7x ≤ 22 x ≥ c
ϵ ‹ |
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pro x > 0: x + 7 ≥
8x -7x ≥
-7 x ≤
1 x ϵ
(0 ; |
pro x < 0: x + 7 ≤
8x -7x ≤
-7 x ≥
1 x ϵ Ø |
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x ϵ (0 ; |
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