Question

15. Match the inequality to its graphed solution.(2 points)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.−5(x+5)>−158x<4x+28−3(x−12)>014(8x+16)>−4

Answer 1

To match inequalities with their graphs, we need to solve each inequality and identify the range of values that it represents. Here's the breakdown of the given inequalities:

1. **−5(x + 5) > −15**:
- Distributing: -5x - 25 > -15
- Adding 25 to both sides: -5x > 10
- Dividing by -5 (remember to flip the inequality): x < -2

2. **8x < 4**:
- Dividing both sides by 8: x < 0.5

3. **x + 28 > 0**:
- Subtracting 28 from both sides: x > -28

4. **−3(x − 12) > 0**:
- Distributing: -3x + 36 > 0
- Subtracting 36 from both sides: -3x > -36
- Dividing by -3 (flip the inequality): x < 12

5. **14(8x + 16) > -4**:
- Distributing: 112x + 224 > -4
- Subtracting 224: 112x > -228
- Dividing by 112: x > -2.0357 (approximately -2)

Now we can pair the inequalities with their graph:

- **x < -2**: Matches the inequality **−5(x + 5) > −15**.
- **x < 0.5:** Matches the inequality **8x < 4**.
- **x > -28:** Matches the inequality **x + 28 > 0**.
- **x < 12:** Matches the inequality **−3(x − 12) > 0**.
- **x > -2.0357:** Matches the inequality **14(8x + 16) > -4**.

You can insert the responses accordingly based on the matching given above.