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andreykadnikov
@andreykadnikov
August 2022
2
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Помогите с номером 2! ВО вложениях!
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m11m
Находим общий знаменатель и дополнительные множители,далее раскрываем скобки,Хы переносим влево,а числа вправо и считаем.
1 votes
Thanks 1
irinan2014
Verified answer
А)
х-1
+
2х-4
> 1¹/₃
3 2
x-1
+
2x-4
-
4
>0
3 2 3
2(x-1)+3(2x-4)-4*2
>0
6
2x-2+6x-12-8 >0
8x-22>0
8x>22
x>22/8
x>2.75
-------------- 2.75
-----------------
\\\\\\\\\\\\\\\\\\
б)
x-4
+
x
≤ -1.(2)
5 7
х-4
+
х
≤
-11
5 7 9
х-4
+
х
+
11
≤ 0
5 7 9
7*9*(х-4) +5*9*х +11*5*7
≤0
5*7*9
63х - 252 +45х +385 ≤ 0
108х +133≤0
108х ≤ -133
х ≤ -133/108
х ≤ - 1 ²⁵/₁₀₈
------------- -1 ²⁵/₁₀₈
---------------
\\\\\\\\\\\\\\
в)
х+2
-
2х-3
<
x
8 5 6
x+2
-
2x-3
-
x
<0
8 5 6
5*6*(x+2)-8*6*(2x-3)-8*5*x
<0
8*5*6
30x+60-96x+144-40x <0
-106x +204 <0
-106x < -204
x> -204/(-106)
x > 102/53
x > 1 ⁴⁹/₅₃
--------- 1 ⁴⁹/₅₃
--------------
\\\\\\\\\\\\\\\
г)
5х-7
-
х
< 2 ¹/₅ -
x
6 9 8
5x-7
-
x
-
11
+
x
< 0
6 9 5 8
9*5*8*(5x-7)-6*5*8x -11*6*9*8 +6*9*5x
<0
6*9*5*8
1800x -2520 - 240x - 4752 +270x <0
1830x -7272 <0
1830x < 7272
x< 7272/1830
x <2424/610
x< 1212/305
x< 3 ²⁹⁷/₃₀₅
-
--------
3 ²⁹⁷/₃₀₅ ---------------
\\\\\\\\\\\
д)
2x+3
+
6x-1
≥
x-5
- 2 ²/₅
5 4 3
2x+3
+
6x-1
-
x-5
+
12
≥ 0
5 4 3 5
4*3*(2x+3)+5*3*(6x-1)-5*4*(x-5)+12*4*3 ≥0
24x+36+90x-15-20x+100+144 ≥0
94x + 265 ≥0
94x ≥ -265
x ≥ -265/94
x ≥ -2 ⁷⁷/₉₄
---------- -2 ⁷⁷/₉₄
---------------
\\\\\\\\\\\\\\\\\\\\\\\
е)
-2х+8
-
2х+1
≤ -6 ²/₃ +
х-1
5 8 4
-2х+8
-
2х+1
+
20
-
х-1
≤ 0
5 8 3 4
8*3*4*(-2х+8)- 5*3*4*(2х+1)+20*5*8*4 - 5*8*3*(х-1)
≤0
5*8*3*4
-192х +768 - 120х -60 + 3200 -120х +120 ≤0
-432х +4028 ≤0
-432х ≤ -4028
х ≥ -4028/(-432)
х ≥ 9 ¹⁴⁰/₄₃₂
х ≥ 9 ⁷⁰/₂₁₆
----------
9 ⁷⁰/₂₁₆ ----------------
\\\\\\\\\\\\\\\\\\\\\\
1 votes
Thanks 1
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Answers & Comments
Verified answer
А) х-1 +2х-4 > 1¹/₃3 2
x-1 + 2x-4 - 4 >0
3 2 3
2(x-1)+3(2x-4)-4*2 >0
6
2x-2+6x-12-8 >0
8x-22>0
8x>22
x>22/8
x>2.75
-------------- 2.75 -----------------
\\\\\\\\\\\\\\\\\\
б) x-4 + x ≤ -1.(2)
5 7
х-4 + х ≤ -11
5 7 9
х-4 + х + 11 ≤ 0
5 7 9
7*9*(х-4) +5*9*х +11*5*7 ≤0
5*7*9
63х - 252 +45х +385 ≤ 0
108х +133≤0
108х ≤ -133
х ≤ -133/108
х ≤ - 1 ²⁵/₁₀₈
------------- -1 ²⁵/₁₀₈ ---------------
\\\\\\\\\\\\\\
в) х+2 - 2х-3 < x
8 5 6
x+2 - 2x-3 - x <0
8 5 6
5*6*(x+2)-8*6*(2x-3)-8*5*x <0
8*5*6
30x+60-96x+144-40x <0
-106x +204 <0
-106x < -204
x> -204/(-106)
x > 102/53
x > 1 ⁴⁹/₅₃
--------- 1 ⁴⁹/₅₃ --------------
\\\\\\\\\\\\\\\
г) 5х-7 - х < 2 ¹/₅ - x
6 9 8
5x-7 - x - 11 + x < 0
6 9 5 8
9*5*8*(5x-7)-6*5*8x -11*6*9*8 +6*9*5x <0
6*9*5*8
1800x -2520 - 240x - 4752 +270x <0
1830x -7272 <0
1830x < 7272
x< 7272/1830
x <2424/610
x< 1212/305
x< 3 ²⁹⁷/₃₀₅
--------- 3 ²⁹⁷/₃₀₅ ---------------
\\\\\\\\\\\
д) 2x+3 +6x-1 ≥ x-5 - 2 ²/₅
5 4 3
2x+3 + 6x-1 - x-5 + 12 ≥ 0
5 4 3 5
4*3*(2x+3)+5*3*(6x-1)-5*4*(x-5)+12*4*3 ≥0
24x+36+90x-15-20x+100+144 ≥0
94x + 265 ≥0
94x ≥ -265
x ≥ -265/94
x ≥ -2 ⁷⁷/₉₄
---------- -2 ⁷⁷/₉₄ ---------------
\\\\\\\\\\\\\\\\\\\\\\\
е) -2х+8 - 2х+1 ≤ -6 ²/₃ + х-1
5 8 4
-2х+8 - 2х+1 + 20 - х-1 ≤ 0
5 8 3 4
8*3*4*(-2х+8)- 5*3*4*(2х+1)+20*5*8*4 - 5*8*3*(х-1) ≤0
5*8*3*4
-192х +768 - 120х -60 + 3200 -120х +120 ≤0
-432х +4028 ≤0
-432х ≤ -4028
х ≥ -4028/(-432)
х ≥ 9 ¹⁴⁰/₄₃₂
х ≥ 9 ⁷⁰/₂₁₆
---------- 9 ⁷⁰/₂₁₆ ----------------
\\\\\\\\\\\\\\\\\\\\\\