1)

[tex]7 < 2x + 3 < 11 \\ 7 - 3 < 2x < 11 - 3 \\ 4 < 2x < 8 \: \: | \div 2 \\ 2 < x < 4 \\ x \: \epsilon \: (2; \: 4)[/tex]

2)

[tex] - 3 < 1 + 2x < 7 \\ - 3 - 1 < 2x < 7 - 1 \\ - 4 < 2x < 6 \: \: | \div 2 \\ - 2 < x < 3 \\ x \: \epsilon \: ( - 2; \: 3)[/tex]

3)

[tex] - 2 < 8 + \frac{x}{7} < 4 \\ - 2 - 8 < \frac{x}{7} < 4 - 8 \\ - 10 < \frac{x}{7} < - 4 \: \: | \times 7 \\ - 70 < x < - 28 \\ x \: \epsilon \: ( - 70; \: - 28)[/tex]

4)

[tex] - 7 < 2x + \frac{1}{2} < 2 \\ - 7 - \frac{1}{2} < 2x < 2 - \frac{1}{2} \\ - 7 \frac{1}{2} < 2x < 1 \frac{1}{2} \: \: | \div 2 \\ - \frac{15}{2 \times 2} < x < \frac{3}{2 \times 2} \\ - \frac{15}{4} < x < \frac{3}{4} \\ - 3.75 <x < 0.75 \\ x \: \epsilon \: ( - 3.75; \: 0.75)[/tex]