Question: Solve the below compound inequality. Write solutions in interval notation.
$x + 10 \geq 6$ and $7x - 1 \geq 6$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is □.
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expr)
B. The solution set is \emptyset.
graph: a horizontal number line is shown across the middle, with no marked solution interval visible; position_hint = center
1. **State the problem:** Solve the compound inequality $$x + 10 \geq 6$$ and $$7x - 1 \geq 6$$ and write the solution in interval notation.
2. **Solve the first inequality:**
$$x + 10 \geq 6$$
Subtract 10 from both sides:
$$x + 10 - 10 \geq 6 - 10$$
$$x \geq -4$$
3. **Solve the second inequality:**
$$7x - 1 \geq 6$$
Add 1 to both sides:
$$7x - 1 + 1 \geq 6 + 1$$
$$7x \geq 7$$
Divide both sides by 7:
$$\frac{\cancel{7}x}{\cancel{7}} \geq \frac{7}{7}$$
$$x \geq 1$$
4. **Combine the inequalities:**
The compound inequality requires both conditions to be true simultaneously:
$$x \geq -4 \quad \text{and} \quad x \geq 1$$
Since $$x$$ must satisfy both, the solution is the intersection of the two intervals:
$$[ -4, \infty ) \cap [1, \infty ) = [1, \infty )$$
5. **Write the solution in interval notation:**
$$[1, \infty )$$
**Final answer:** The solution set is $$[1, \infty )$$.