DO ZADANIA:
1. Pamiętaj o narysowaniu osi x
2. Znak " / " oznacza że coś jest pod ułamkiem :-) np. (12-3x)/3 :czyt. (12-3x) jest w liczniku, a w mianowniku 3
A)
(12-3x)/3 + x - (3x-2)/4 ≥ -5
(4×(12-3x))/12 + (12x)/12 - (3×(3x-2))/12 ≥ -5
(48 - 12x + 12x - 9x +6)/12 ≥ -5
(54-9x)/12 ≥ -5 |× 12
54-9x ≥ -60
-9x ≥ -60 - 54
-9x ≥ -114 |÷ (-9)
x ≤ 114/9
x ≤ 38/3
B)
(10z-2)/3 - (6z+2)/2 - (4z-5)/6 > 0
(2×(10z-2)) - 3(6z+2) - (4z-5))/6 > 0
(20z - 4 - 18z -4 -4z +5)/6 > 0
(-2z-3)/6>0 |×6
-2z-3 > 0
-2z > 3 |÷(-2)
z < -³/₂
C)
(2x-4-3x)/5 -(7x)/2 + x +3 < 0
(2×(2x-4-3x)-5(7x)+10x+30)/10 < 0
(4x-8-6x-35x+10x+30)/10 < 0
(-27x-22)/10 < 0 |×10
-27x-22 < 0
-27x < 22
x > - ²²/₂₇
D)
y/2 - (3y)/4 > 3-(-5-y)/3×½
y/2 - (3y)/4 > 3-(-2,5-0,5y)/3
y/2 - (3y)/4 - (2,5+0,5y)/3 > 3
(6y-9y-10-2y)/12 > 3
(-5y-10)/12 > 3 |×12
-5y-10 > 36
-5y > 46 |÷(-5)
y < - ⁴⁶/₅
y < -9¹/₅