1)
|4x-5| ≤ 3
a)
|4x-5| = 4x - 5 daca 4x -5 ≥ 0 => x ≥ 5/4
4x - 5 ≤ 3
4x ≤ 8
x ≤ 8 / 4
x ≤ 2 si x ≥ 5/4
=> x ∈ [5/4, 2]
b)
|4x-5| = -(4x - 5) daca 4x -5 < 0 => x < 5/4
5 - 4x ≤ 3
-4x ≤ 3-5
-4x ≤ -2 | * (-1)
4x ≥ 2
x ≥ 2/4
x ≥ 1/2 si x < 5/4
=> x ∈ [1/2, 5/4 )
Solutia:
x ∈ [1/2, 5/5 ) U [5/4, 2]
x ∈ [1/2, 2]
2)
x² - 6x + 9 ≤ 0
(x - 3)(x - 3) = 0
=> x₁ = x₂ = 3 este o solutie dubla
facorul lui x² > 0
=> functia atasata inecuatiei nu are valori negative
dar are valoarea 0 in x = 3
Solutia inecuatiei:
x = 0