To solve the inequality \( 22 + x \geq -7 \):

1. **Isolate** \( x \) by subtracting 22 from both sides:
   \[
   x \geq -7 - 22
   \]
   \[
   x \geq -29
   \]

This means that for the inequality \( 22 + x \geq -7 \) to be true, \( x \) must be greater than or equal to \(-29\).

However, you have also provided \( x \geq -15 \). So the overall solution must satisfy both conditions:

\[
x \geq -29 \quad \text{and} \quad x \geq -15
\]

Since \( x \) must be at least \(-15\) to satisfy both inequalities, the final solution is:

\[
x \geq -15
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would the solution change if the inequality was \( 22 + x > -7 \)?
2. What is the solution set if the inequality is \( 22 + x \leq -7 \)?
3. How can you graph the solution \( x \geq -15 \) on a number line?
4. What is the effect of adding a constant to both sides of an inequality?
5. How does multiplying or dividing both sides of an inequality by a negative number change the inequality?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide both sides by a negative number.

Learn how to solve and understand the inequality 22 + x ≥ –7; x ≥ –15 with a step-by-step explanation. This problem involves key concepts in inequalities and linear equations. Suitable for students in Grades 7-9.

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