7a)
5x - 2 ≥ 13
5x ≥ 13 + 2
5x ≥ 15
x ≥ 15 / 5
x ≥ 3
x ∈ {3, ∞)
7b)
8 - 4x > -32
-4x > -32 - 8
-4x > -40
4x < 40
x < 40 / 10
x < 4
x ∈ (-∞, 4)
7c)
2(1 - x) ≥ 4(3x + 2)
2 - 2x ≥ 12x + 8
-2x - 12x ≥ 8 - 2
-14x ≥ 6
14x ≤ -6
x ≤ -6 / 14
x ≤ -3 / 7
x ∈ (-∞, -3/7]
7d)
2 - 3(x + 2) ≤ 5 - 2x
2 - 3x - 6 ≤ 5 - 2x
-3x + 2x ≤ 5 + 6 - 2
-x ≤ 9
x ≥ -9
x ∈ [-9, ∞)
9a)
-3x > 9
4x < 1
---
3x < -9
4x < -1
---
x < -9 / 3 => x < -3
x < -1 / 4 => x < -0,25
---
-3 < -0,25
=> x < -3
x ∈ (-∞, -3)
9b)
11x + 1 ≥ -5
2 - 3x < 5
---
11x ≥ -5 - 1
-3x < 5 - 2
---
11x ≥ -6
-3x < 3
---
11x ≥ - 6
3x > -3
---
x ≥ -6 / 11
x > -3 / 3
---
x ≥ -6 / 11
x > -1
---
-6 / 11 > -1
=> x ≥ -6 / 11
x ∈ [-6/11, ∞)
9c)
3 - 4x > 5
6 + 9x ≤ 1
---
-4x > 5 - 3
9x ≤ 1 - 6
---
-4x > 2
9x ≤ -5
---
4x < -2
9x ≤ -5
---
x < -2 / 4
x ≤ -5 / 9
---
x < -1 / 2
x ≤ -5 / 9
---
-5 / 9 < -1 / 2
=> x ≤ -5 / 9
x ∈ (-∞, -5 / 9]
9d)
3x - 6 > 2x
2x - 6 > 5x
---
3x - 2x > 6
2x - 5x > 6
---
x > 6
-3x > 6
---
x > 6
3x < -6
---
x > 6
x < -6/3
---
x > 6
x < -2
Acest sistem de inecuatii nu are solutie
9e)
2x + 1 ≤ 13
9 - 2x < x
---
2x ≤ 13 - 1
-2x - x < -9
---
2x ≤ 12
-3x < - 9
---
2x ≤ 12
3x > 9
---
x ≤ 12 / 2
x > 9 / 3
---
x ≤ 6
x > 3
---
x ∈ (3, 6]
