The problem asks us to match the given inequalities with their corresponding number line representations. Each number line has two inequalities that represent it. We need to solve each inequality and identify the appropriate number line.

1. Problem Description

The problem asks us to match the given inequalities with their corresponding number line representations. Each number line has two inequalities that represent it. We need to solve each inequality and identify the appropriate number line.

2. Solution Steps

A. $2x + 4 > 10$

$2x > 10 - 4$

$2x > 6$

$x > 3$

B. $x \le -2$

C. $18 \ge 5x + 3$

$15 \ge 5x$

$3 \ge x$

$x \le 3$

D. $x \ge 3$

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

$4x + 8 \le -4$

$4x \le -12$

$x \le -3$

F. $-4x + 5 > 13$

$-4x > 8$

$x < -2$ (Dividing by a negative number flips the inequality)

G. $-3x > -9$

$x < 3$ (Dividing by a negative number flips the inequality)

H. $5x + 6 \ge 21$

$5x \ge 15$

$x \ge 3$

I. $2x - 4 < -10$

$2x < -6$

$x < -3$

J. $8 \le 4x + 20$

$-12 \le 4x$

$-3 \le x$

$x \ge -3$

K. $x < -3$

L. $x < 3$

M. $x \le -3$

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

$4x - 16 \le -24$

$4x \le -8$

$x \le -2$

O. $x > 3$

P. $x > -3$

Q. $x < -2$

R. $x \le 3$

S. $x \ge -3$

T. $4 - 2x < 10$

$-2x < 6$

$x > -3$

Now we need to match the inequalities with the number lines. Note that each number line represents two inequalities.

Looking at the number lines, we can make the following matches (Note: the order of the two letters in the pairs below does not matter because the question asks to match the inequality to the number lines):

Number line 1: A ($x>3$) and O ($x>3$)

Number line 2: B ($x \le -2$) and N ($x \le -2$)

Number line 3: C ($x \le 3$) and R ($x \le 3$)

Number line 4: D ($x \ge 3$) and H ($x \ge 3$)

Number line 5: E ($x \le -3$) and M ($x \le -3$)

Number line 6: F ($x < -2$) and Q ($x < -2$)

Number line 7: G ($x < 3$) and L ($x < 3$)

Number line 8: I ($x < -3$) and K ($x < -3$)

Number line 9: J ($x \ge -3$) and S ($x \ge -3$)

Number line 10: P ($x > -3$) and T ($x > -3$)

3. Final Answer

A and O match number line

1. B and N match number line

2. C and R match number line

3. D and H match number line

4. E and M match number line

5. F and Q match number line

6. G and L match number line

7. I and K match number line

8. J and S match number line

9. P and T match number line

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