The problem consists of solving two sets of inequalities. (1) is a system of inequalities: $8x - 15 < 4x - 35$ $0.3x + 1 > 0.5x - 0.2$ (2) is a compound inequality: $x - 5 < 2x \le 6 - x$

1. Problem Description

The problem consists of solving two sets of inequalities.

(1) is a system of inequalities:

$8x - 15 < 4x - 35$

$0.3x + 1 > 0.5x - 0.2$

(2) is a compound inequality:

$x - 5 < 2x \le 6 - x$

2. Solution Steps

(1) Solving the system of inequalities:

First inequality:

$8x - 15 < 4x - 35$

$8x - 4x < -35 + 15$

$4x < -20$

$x < -5$

Second inequality:

$0.3x + 1 > 0.5x - 0.2$

$1 + 0.2 > 0.5x - 0.3x$

$1.2 > 0.2x$

$0.2x < 1.2$

$x < \frac{1.2}{0.2}$

$x < 6$

Combining the inequalities $x < -5$ and $x < 6$, we take the more restrictive condition, which is $x < -5$.

Therefore, the answer for 30 is -

5.

(2) Solving the compound inequality:

$x - 5 < 2x \le 6 - x$

This can be split into two inequalities:

$x - 5 < 2x$ and $2x \le 6 - x$

First inequality:

$x - 5 < 2x$

$-5 < 2x - x$

$-5 < x$

$x > -5$

Second inequality:

$2x \le 6 - x$

$2x + x \le 6$

$3x \le 6$

$x \le 2$

Combining the inequalities $x > -5$ and $x \le 2$, we have $-5 < x \le 2$.

Therefore, the answer for 31-1 is -5, and the answer for 31-2 is

2.

3. Final Answer

30: -5

31-1: -5

31-2: 2