Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. match each compound inequality on the left to the graph that represents its solution on the right. $4x + 3 > 15$ or $-6x \geq 12$; $-8x > -24$ and $-10 \leq 2x - 6$; $-29 \leq 9x - 2 < 16$; click and hold an item in one column, then drag it to the matching item in the other column. be sure your cursor is over the target before releasing. need help? watch this video.

Explanation:

Step1: Solve \(4x + 3>15\) or \(-6x\geq12\)

- Solve \(4x + 3>15\):
Subtract 3 from both sides: \(4x>15 - 3=12\)
Divide by 4: \(x > 3\)
- Solve \(-6x\geq12\):
Divide by - 6 (reverse inequality): \(x\leq - 2\)
So the solution is \(x > 3\) or \(x\leq - 2\)

Step2: Solve \(-8x>-24\) and \(-10\leq2x - 6\)

- Solve \(-8x>-24\):
Divide by - 8 (reverse inequality): \(x < 3\)
- Solve \(-10\leq2x - 6\):
Add 6 to both sides: \(-4\leq2x\)
Divide by 2: \(-2\leq x\)
So the solution is \(-2\leq x<3\)

Step3: Solve \(-29\leq9x - 2<16\)

- Add 2 to all parts: \(-29 + 2\leq9x<16 + 2\)
\(-27\leq9x<18\)
- Divide by 9: \(-3\leq x<2\)

Now, match the solutions to the graphs:
- For \(4x + 3>15\) or \(-6x\geq12\) (solution \(x > 3\) or \(x\leq - 2\)): The graph with open circle at 3 (for \(x>3\)) and closed circle at - 2 (for \(x\leq - 2\)) (the second graph from the top? Wait, let's check the x - values. Wait, the first graph (top) has closed at - 3? No, wait the first graph (top) has closed at - 3? Wait no, the first graph (top) has closed at - 3? Wait no, looking at the graphs:

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Answer:

Step1: Solve \(4x + 3>15\) or \(-6x\geq12\)

• Solve \(4x + 3>15\):

Subtract 3 from both sides: \(4x>15 - 3=12\)
Divide by 4: \(x > 3\)

• Solve \(-6x\geq12\):

Divide by - 6 (reverse inequality): \(x\leq - 2\)
So the solution is \(x > 3\) or \(x\leq - 2\)

Step2: Solve \(-8x>-24\) and \(-10\leq2x - 6\)

• Solve \(-8x>-24\):

Divide by - 8 (reverse inequality): \(x < 3\)

• Solve \(-10\leq2x - 6\):

Add 6 to both sides: \(-4\leq2x\)
Divide by 2: \(-2\leq x\)
So the solution is \(-2\leq x<3\)

Step3: Solve \(-29\leq9x - 2<16\)

• Add 2 to all parts: \(-29 + 2\leq9x<16 + 2\)

\(-27\leq9x<18\)

• Divide by 9: \(-3\leq x<2\)

Now, match the solutions to the graphs:

• For \(4x + 3>15\) or \(-6x\geq12\) (solution \(x > 3\) or \(x\leq - 2\)): The graph with open circle at 3 (for \(x>3\)) and closed circle at - 2 (for \(x\leq - 2\)) (the second graph from the top? Wait, let's check the x - values. Wait, the first graph (top) has closed at - 3? No, wait the first graph (top) has closed at - 3? Wait no, the first graph (top) has closed at - 3? Wait no, looking at the graphs:

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