Question

Match the inequality to its graphed solution.
The first number line has an open circle on 12 and the arrow moves left
The second number line has an open circle on -2 and the arrow moves left

Answer 1

the equation dummy

Answer 2

Match the inequality EQUATION

Answer 3

dummy.
1. 8x < 4x + 28
2. -5 (x + 5) > -15
3. 1/4 (8x + 16) > -4
4. -3 (x - 12) > 0

Answer 4

The two inequalities corresponding to the described number lines are:

1. For the first number line with an open circle on 12 and the arrow moving left, the inequality is \( x < 12 \). This represents all numbers less than 12.

2. For the second number line with an open circle on -2 and the arrow moving left, the inequality is \( x < -2 \). This represents all numbers less than -2.

So:

- First number line: \( x < 12 \)
- Second number line: \( x < -2 \)

Answer 5

I apologize for misunderstanding your request earlier. Here are the correct inequalities associated with the graphed solutions described:

1. The first number line with an **open circle on 12** and an arrow moving **left** represents the inequality:

**\( x < 12 \)**

2. The second number line with an **open circle on -2** and an arrow moving **left** represents the inequality:

**\( x < -2 \)**

If the request was specifically for the equations (not inequalities) that correspond to these graphical representations, inequalities themselves do not represent equations but conditions. However, these inequalities are indeed what match the described graphs.

If you meant something else by "the equation," please clarify, and I would be happy to assist further!

Answer 6

I apologize for the confusion! Here are the matched inequality equations based on the number line descriptions you provided:

1. **First Number Line**: Open circle on 12 with an arrow moving left corresponds to the equation:

**\( x = 12 \)**

(This indicates the boundary point, but we commonly interpret it as \( x < 12 \)).

2. **Second Number Line**: Open circle on -2 with an arrow moving left corresponds to the equation:

**\( x = -2 \)**

(Again, indicating the boundary point, but interpreted as \( x < -2 \)).

So to clarify:

- **First Number Line (Open circle on 12)**: **\( x = 12 \)**
- **Second Number Line (Open circle on -2)**: **\( x = -2 \)**

These are the equations representing the boundary points of each inequality. Thank you for your patience, and I hope this matches what you were looking for!

Answer 7

Thank you for your patience! Let's solve each inequality step by step and match them with their corresponding equations based on the provided options.

### 1. \(8x < 4x + 28\)
**Solve for \(x\)**:
\[
8x - 4x < 28 \\
4x < 28 \\
x < 7
\]
**Corresponding equation**: \(x = 7\)

### 2. \(-5(x + 5) > -15\)
**Solve for \(x\)**:
\[
-5x - 25 > -15 \\
-5x > -15 + 25 \\
-5x > 10 \\
x < -2 \quad (\text{remember to flip the inequality when dividing by a negative})
\]
**Corresponding equation**: \(x = -2\)

### 3. \(\frac{1}{4}(8x + 16) > -4\)
**Solve for \(x\)**:
\[
8x + 16 > -4 \quad (\text{multiply both sides by 4})\\
8x > -4 - 16 \\
8x > -20 \\
x > -\frac{5}{2} \quad (or -2.5)
\]
**Corresponding equation**: \(x = -\frac{5}{2}\)

### 4. \(-3(x - 12) > 0\)
**Solve for \(x\)**:
\[
-3x + 36 > 0 \\
-3x > -36 \\
x < 12 \quad (\text{again, remember to flip the inequality})
\]
**Corresponding equation**: \(x = 12\)

### Summary of Matches:
1. **\(8x < 4x + 28\)** corresponds to **\(x = 7\)**
2. **\(-5(x + 5) > -15\)** corresponds to **\(x = -2\)**
3. **\(\frac{1}{4}(8x + 16) > -4\)** corresponds to **\(x = -\frac{5}{2}\)**
4. **\(-3(x - 12) > 0\)** corresponds to **\(x = 12\)**

If you need further assistance, let me know!