Question

7)
<---(black line with filled dot at -10)----(open dot at -4)---(black line)---(open dot at 1)----(open dot at 6)---(black line)--->

Explanation:

To solve the inequality represented by the number line, we analyze each segment:

Step 1: Analyze the left segment (closed dot at \(-10\))

The closed dot at \(-10\) and the arrow pointing left means \(x \leq -10\).

Step 2: Analyze the middle segment (open dots at \(-4\) and \(1\))

The open dots at \(-4\) and \(1\) with the line between them means \(-4 < x < 1\).

Step 3: Analyze the right segment (open dot at \(6\))

The open dot at \(6\) and the arrow pointing right means \(x > 6\).

Combining these intervals, the solution to the inequality is:

$$ x \leq -10 \quad \text{or} \quad -4 < x < 1 \quad \text{or} \quad x > 6 $$

\(\boxed{x \leq -10 \text{ or } -4 < x < 1 \text{ or } x > 6}\)

Answer:

To solve the inequality represented by the number line, we analyze each segment:

Step 1: Analyze the left segment (closed dot at \(-10\))

The closed dot at \(-10\) and the arrow pointing left means \(x \leq -10\).

Step 2: Analyze the middle segment (open dots at \(-4\) and \(1\))

The open dots at \(-4\) and \(1\) with the line between them means \(-4 < x < 1\).

Step 3: Analyze the right segment (open dot at \(6\))

The open dot at \(6\) and the arrow pointing right means \(x > 6\).

Combining these intervals, the solution to the inequality is:

$$ x \leq -10 \quad \text{or} \quad -4 < x < 1 \quad \text{or} \quad x > 6 $$

\(\boxed{x \leq -10 \text{ or } -4 < x < 1 \text{ or } x > 6}\)