Раскрываем модуль1)lxl+3x=12x ≥ 0x + 3x = 124x = 12x₁ = 3 даx < 0-x + 3x = 122x = 12x = 6 нет2)
lxl-4x=9x ≥ 0x - 4x = 9-3x = 9x = -3 нетx < 0-x - 4x = 9-5x = 9x₁ = -9/5 да3)
2(x-5)-6lxl=-16x ≥ 02(x-5)-6x=-162x - 10 - 6x = -16-4x = -6x₁ = 3/2 даx < 02(x-5)+6x=-162x - 10 + 6x = -168x = -6x₂ = -3/4 да
Раскрываем модуль
1)
lxl+3x=12
x ≥ 0
x + 3x = 12
4x = 12
x₁ = 3 да
x < 0
-x + 3x = 12
2x = 12
x = 6 нет
2)
lxl-4x=9
x ≥ 0
x - 4x = 9
-3x = 9
x = -3 нет
x < 0
-x - 4x = 9
-5x = 9
x₁ = -9/5 да
3)
2(x-5)-6lxl=-16
x ≥ 0
2(x-5)-6x=-16
2x - 10 - 6x = -16
-4x = -6
x₁ = 3/2 да
x < 0
2(x-5)+6x=-16
2x - 10 + 6x = -16
8x = -6
x₂ = -3/4 да