The problem is to match each inequality with its corresponding number line representation.

1. Problem Description

The problem is to match each inequality with its corresponding number line representation.

2. Solution Steps

First, we solve each inequality for $x$.

A: $2x + 4 > 10$

$2x > 10 - 4$

$2x > 6$

$x > 3$

This corresponds to the number line 'o', which has an open circle at 3 and shading to the right.

B: $x \le -2$

This corresponds to the number line 'q', which has a closed circle at -2 and shading to the left.

C: $18 \ge 5x + 3$

$15 \ge 5x$

$3 \ge x$ or $x \le 3$

This corresponds to the number line 'r', which has a closed circle at 3 and shading to the left.

D: $x \ge 3$

This corresponds to the number line 's', which has a closed circle at 3 and shading to the right.

E: $4(x+2) \le -4$

$4x + 8 \le -4$

$4x \le -12$

$x \le -3$

This corresponds to the number line 'm', which has a closed circle at -3 and shading to the left.

F: $-4x + 5 > 13$

$-4x > 8$

$x < -2$

This corresponds to the number line 'p', which has an open circle at -2 and shading to the left.

G: $-3x > -9$

$x < 3$

This corresponds to the number line 'l', which has an open circle at 3 and shading to the left.

H: $5x + 6 \ge 21$

$5x \ge 15$

$x \ge 3$

This corresponds to the number line 's', which has a closed circle at 3 and shading to the right.

I: $2x - 4 < -10$

$2x < -6$

$x < -3$

This corresponds to the number line 'k', which has an open circle at -3 and shading to the left.

J: $8 \le 4x + 20$

$-12 \le 4x$

$-3 \le x$ or $x \ge -3$

This corresponds to the number line 't', which has a closed circle at -3 and shading to the right.

N: $4(x-4) \le -24$

$4x - 16 \le -24$

$4x \le -8$

$x \le -2$

This corresponds to the number line 'q', which has a closed circle at -2 and shading to the left.

O: $x>3$

This corresponds to the number line 'o', which has an open circle at 3 and shading to the right.

P: $x>-3$

The corresponding number line has an open circle at -3 and is shaded to the right. None of the given graphs match.

Q: $x<-2$

This corresponds to the number line 'p', which has an open circle at -2 and shading to the left.

R: $x \le 3$

This corresponds to the number line 'r', which has a closed circle at 3 and shading to the left.

S: $x \ge -3$

This corresponds to the number line 't', which has a closed circle at -3 and shading to the right.

T: $4 - 2x < 10$

$-2x < 6$

$x > -3$

This corresponds to the number line that has an open circle at -3 and shading to the right. None of the given graphs match, but 'b' seems closest.

The matches are as follows:

A - o

B - q

C - r

D - s

E - m

F - p

G - l

H - s

I - k

J - t

N - q

O - o

Q - p

R - r

S - t

T - b

3. Final Answer

A - o

B - q

C - r

D - s

E - m

F - p

G - l

H - s

I - k

J - t

N - q

O - o

Q - p

R - r

S - t

T - b