1.
x
>
2
3
(
x
−
1
)
a
n
d
−
2
x
≥
1
6
−
1
1
3
x
{\displaystyle \ x>{\frac {2}{3}}(x-1)\quad and\quad -2x\geq {\frac {1}{6}}-1{\frac {1}{3}}x}
2.
x
4
−
1
+
2
x
>
8
x
+
3
4
a
n
d
x
+
5
3
+
x
−
1
<
4
x
−
4
4
{\displaystyle \ {\frac {x}{4}}-1+2x>{\frac {8x+3}{4}}\quad and\quad {\frac {x+5}{3}}+x-1<{\frac {4x-4}{4}}}
3.
5
(
x
+
1
)
>
1
−
3
x
+
7
(
x
+
1
)
a
n
d
x
+
1
6
+
x
2
<
1
2
(
x
+
2
)
{\displaystyle \ 5(x+1)>1-3x+7(x+1)\quad and\quad {\frac {x+1}{6}}+{\frac {x}{2}}<{\frac {1}{2}}(x+2)}
4.
x
+
4
>
x
+
1
2
a
n
d
5.5
>
11
−
x
2
{\displaystyle \ x+4>{\frac {x+1}{2}}\quad and\quad 5.5>{\frac {11-x}{2}}}
5.
4.5
−
x
3
>
1
1
6
a
n
d
3
(
x
+
1
)
−
5
(
x
−
1
)
>
16
{\displaystyle \ {\frac {4.5-x}{3}}>1{\frac {1}{6}}\quad and\quad 3(x+1)-5(x-1)>16}
6.
−
7
(
x
−
2
)
+
2
(
x
+
1
)
3
<
13
a
n
d
(
4
−
2
x
)
(
x
+
5
)
<
−
2
(
x
2
+
4
x
−
10
)
+
1
{\displaystyle \ -{\frac {7(x-2)+2(x+1)}{3}}<13\quad and\quad (4-2x)(x+5)<-2(x^{2}+4x-10)+1}
7.
6
−
2
x
<
3
x
4
+
2
(
1
−
x
)
a
n
d
−
(
3
(
x
−
2
)
7
+
1
)
<
16
7
{\displaystyle \ 6-2x<{\frac {3x}{4}}+2(1-x)\quad and\quad -\left({\frac {3(x-2)}{7}}+1\right)<{\frac {16}{7}}}
8.
7
(
x
−
3
)
+
5
(
3
−
x
)
<
−
14
a
n
d
7
>
5
(
2
−
x
)
+
3
(
x
+
1
)
{\displaystyle \ 7(x-3)+5(3-x)<-14\quad and\quad 7>5(2-x)+3(x+1)}
9.
3
(
x
+
2
)
+
1
<
4
x
+
5
≤
x
+
2
(
x
+
5
)
a
n
d
x
≥
2
(
5
−
x
)
{\displaystyle \ 3(x+2)+1<4x+5\leq x+2(x+5)\quad and\quad x\geq 2(5-x)}
10.
2
(
3
−
x
)
+
2
(
x
−
5
)
<
x
<
1
a
n
d
2
−
7
x
4
+
x
≤
2
x
+
1
2
{\displaystyle \ 2(3-x)+2(x-5)<x<1\quad and\quad {\frac {2-7x}{4}}+x\leq {\frac {2x+1}{2}}}
11.
x
+
8
5
>
1
a
n
d
5
−
2
x
>
10
+
2
x
2
a
n
d
x
−
3
2
<
2
{\displaystyle \ {\frac {x+8}{5}}>1\quad and\quad 5-2x>{\frac {10+2x}{2}}\quad and\quad {\frac {x-3}{2}}<2}
12.
7
(
x
+
1
)
<
8
x
+
1
a
n
d
5
+
2
x
<
5
x
+
2
2
≤
2
(
x
+
3
)
a
n
d
19
−
2
x
<
0
{\displaystyle \ 7(x+1)<8x+1\quad and\quad 5+2x<{\frac {5x+2}{2}}\leq 2(x+3)\quad and\quad 19-2x<0}
13.
2
(
2
−
x
)
<
8
−
2
x
a
n
d
4
x
+
32
8
>
6
x
+
24
12
{\displaystyle \ 2(2-x)<8-2x\quad and\quad {\frac {4x+32}{8}}>{\frac {6x+24}{12}}}
