The problem asks us to solve two sets of inequalities and find the values that fill in the boxes. (1) Solve the system of inequalities: $8x - 15 < 4x - 35$ $0.3x + 1 > 0.5x - 0.2$ and express the solution as $x <$ box 30. (2) Solve the compound inequality: $x - 5 < 2x \le 6 - x$ and express the solution as $-$(box 31-1) $< x \le$ box 31-2.

1. Problem Description

The problem asks us to solve two sets of inequalities and find the values that fill in the boxes.

(1) Solve the system of inequalities:

$8x - 15 < 4x - 35$

$0.3x + 1 > 0.5x - 0.2$

and express the solution as $x <$ box

3

0.

(2) Solve the compound inequality:

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

and express the solution as $-$(box 31-1) $< x \le$ box 31-

2.

2. Solution Steps

(1)

Solve the first inequality:

$8x - 15 < 4x - 35$

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

$4x < -20$

$x < -5$

Solve the second inequality:

$0.3x + 1 > 0.5x - 0.2$

$1 + 0.2 > 0.5x - 0.3x$

$1.2 > 0.2x$

$0.2x < 1.2$

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

$x < 6$

Since both inequalities must be true, we take the more restrictive solution: $x < -5$. Thus, box 30 is filled with -

5.

(2)

Solve the compound inequality $x - 5 < 2x \le 6 - x$. We can break this into two inequalities:

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

Solving the first inequality:

$x - 5 < 2x$

$-5 < 2x - x$

$-5 < x$

$x > -5$

Solving the second inequality:

$2x \le 6 - x$

$2x + x \le 6$

$3x \le 6$

$x \le 2$

Combining the solutions $x > -5$ and $x \le 2$, we get $-5 < x \le 2$.

Thus, box 31-1 is filled with 5 and box 31-2 is filled with

2.

3. Final Answer

The value for box 30 is -

5. The value for box 31-1 is

5. The value for box 31-2 is

2.