We are given that $a < b$. We need to determine the correct inequality sign (either $<$ or $>$) to fill in the blanks for the following expressions: (1) $a - 5 \square b - 5$ (2) $\frac{1}{2}a - 3 \square \frac{1}{2}b - 3$ (3) $6 - a \square 6 - b$ (4) $-\frac{a}{7} \square -\frac{b}{7}$

1. Problem Description

We are given that $a < b$. We need to determine the correct inequality sign (either $<$ or $>$) to fill in the blanks for the following expressions:

(1) $a - 5 \square b - 5$

(2) $\frac{1}{2}a - 3 \square \frac{1}{2}b - 3$

(3) $6 - a \square 6 - b$

(4) $-\frac{a}{7} \square -\frac{b}{7}$

2. Solution Steps

(1) Since $a < b$, subtracting 5 from both sides preserves the inequality:

$a - 5 < b - 5$.

So the correct sign for 24 is $<$, which corresponds to option ア.

(2) Since $a < b$, multiplying both sides by $\frac{1}{2}$ (a positive number) preserves the inequality:

$\frac{1}{2}a < \frac{1}{2}b$.

Subtracting 3 from both sides preserves the inequality:

$\frac{1}{2}a - 3 < \frac{1}{2}b - 3$.

So the correct sign for 25 is $<$, which corresponds to option ア.

(3) Since $a < b$, multiplying both sides by -1 reverses the inequality:

$-a > -b$.

Adding 6 to both sides preserves the inequality:

$6 - a > 6 - b$.

So the correct sign for 26 is $>$, which corresponds to option イ.

(4) Since $a < b$, multiplying both sides by $-\frac{1}{7}$ (a negative number) reverses the inequality:

$-\frac{a}{7} > -\frac{b}{7}$.

So the correct sign for 27 is $>$, which corresponds to option イ.

3. Final Answer

24: ア

25: ア

26: イ

27: イ