Решите пожалуйста эти неравенства и как их можно показать на числовой прямой?
2(x – 1) < 3(2 – x)
-3 ≤ 2x – 1 ≤ 5
-3 x2 – 10x – 3 ≤ 0
2(x – 1) < 3(2 – x)
-3 ≤ 2x – 1 ≤ 5
-3 x2 – 10x – 3 ≤ 0
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Verified answer
1) 2x-2<6-3x2x+3x<6+2
5x<8
x<8/5
x<1,6
////////////
---------₀--------->x
1,6
x∈(-∞; 1,6)
2) -3+1≤2x≤5+1
-2≤2x≤6
-2/2≤x≤6/2
-1≤x≤3
xxxxxx
----------.---------.----->x
-1 3
x∈[-1; 3]
3) D=100-36=64
x₁ = 10-8 / -6 = -1/3
x₂ = 10+8 / -6 = -3
+ - +
----------.-----------.-------->x
-3 -1/3
x∈[-3; -1/3]
Verified answer
Решите пожалуйста эти неравенства и как их можно показать на числовой прямой?2(x – 1) < 3(2 – x)-3 ≤ 2x – 1 ≤ 5
-3 x2 – 10x – 3 ≤ 0
1)
2(x – 1) < 3(2 – x) ⇔2x -2< 6 – 3x ⇔ 5x < 8 ⇔ x < 8 /5
------////////////------ 8 /5------------------------------------
2)
-3 ≤ 2x – 1 ≤ 5 ⇔ -3+1 ≤ 2x – 1+1 ≤ 5 +1 ⇔
-2≤ 2x ≤ 6 ⇔ -2/2≤ 2x /2 ≤ 6/2 ⇔ -1≤ x ≤ 3
----------------------------------[(-1)////////////////(3)]------------------------
3) -3 x² – 10x – 3 ≤ 0 ⇔ 3x²+10x+3≥0
3x²+10x+3=0
D=100-4·3·3=64=8²
x1=(-10-8)/6=-3 x2=(-10+8)/6= -1/3
+ - +
///////////////](-3 )-------------------[( -1/3 )////////////////////-
x∈(-∞,-3]∪[-1/3, +∞)