17)
[tex]\frac{2x+5}{4} < x < \frac{3x+13}{6} [/tex]
[tex]\frac{2x+5}{4} < x [/tex]
[tex]2x+5 < 4x\\
5 < 2x\\
\frac{5}{2} < x\\
\\
x < \frac{3x+13}{6}\\
6x < 3x + 13\\
3x < 13\\
x < \frac{13}{3} \\[/tex]
x ∈{3,4}
18)
[tex]x - 1 < \frac{3x + 7}{4} < x + 2 \\
\\
x - 1 < \frac{3x+7}{4}\\
\\
4x - 4 < 3x + 7\\
\\
4x < 3x + 11\\
x < 11\\[/tex]
[tex]\frac{3x+7}{4}
x ∈ {10, 9, 8, 7, 6, 5, 4, 3, 2, 1}
19)
Multimea A:
[tex]x-2<\frac{2x+3}{7}
[tex]x - 2<\frac{2x+3}{7} \\
\\
7x - 14 < 2x + 3\\
\\
7x < 2x + 17\\
\\
5x < 17\\\\
\\
x < \frac{17}{5} [/tex]
[tex]\frac{2x+3}{7} < x + 3\\
2x + 3 < 7x + 21\\
2x < 7x + 18\\
0 < 5x + 18\\
-18<5x\\
5x>-18\\
x>\frac{-18}{5} [/tex]
A = {-3, -2, -1, 0, 1, 2, 3}
Multimea B:
[tex]x - 1<\frac{4x+1}{3} \leq x+2\\[/tex]
[tex]x-1<\frac{4x+1}{3} \\
\\
3x - 3 < 4x + 1\\
3x < 4x + 4\\
\\
0 < x + 4\\
-4 < x[/tex]
[tex]\frac{4x+1}{3}\leq x+2\\
\\
4x + 1 \leq 3x + 6\\
4x\leq 3x+5\\
x\leq 5[/tex]
B = {-3, -2, -1, 1, 2, 3, 4, 5}
A ∩ B = {-3, -2, -1, 1, 2, 3}
20)
[tex]\frac{2x+3}{2} \leq \frac{3(x+3)}{5}<\frac{4x+13}{6} [/tex]
[tex]\frac{2x+3}{2}\leq \frac{3(x+3)}{5} \\
\\
\frac{2x+3}{2} * 10\leq \frac{3(x+3)}{5}*10\\
\\
5(2x+3)\leq 2*3(x+3)\\
10x+15\leq 6x+18\\
10x\leq 6x+3\\
4x\leq 3\\
x\leq \frac{3}{4} [/tex]
[tex]\frac{3(x+3)}{5}<\frac{4x+13}{6} \\
\\
\frac{3(x+3)}{5}*30<\frac{4x+13}{6} *30\\
18(x+3)<5(4x+13)\\
18x+54<20x+65\\
54<2x+65\\
-11<2x\\
\frac{-11}{2}
[tex](\frac{-11}{2} , \frac{3}{4}] [/tex]
