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Let's solve the given inequality step by step.

### (a) Solve the inequality:

\[
\frac{-x}{2} < 1
\]

1. Multiply both sides of the inequality by 2 to eliminate the fraction:

\[
-x < 2
\]

2. Now, divide both sides by \(-1\). Remember, when dividing or multiplying an inequality by a negative number, the direction of the inequality reverses:

\[
x > -2
\]

So, the solution to the inequality is:

\[
x > -2
\]

### (b) State the largest integer that satisfies the inequality:

Since the inequality is \(x > -2\), the largest integer that satisfies this inequality is **1**.

Let me know if you'd like further details!

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Here are some related questions:

1. What happens when you multiply both sides of an inequality by a negative number?
2. Can you provide an example of solving an inequality with a different variable?
3. What is the general process for solving inequalities involving fractions?
4. How does flipping the inequality sign affect the solution?
5. What are the differences between solving equalities and inequalities?

**Tip**: Always remember to reverse the inequality sign when multiplying or dividing by a negative number in inequalities.

Solve the inequality -x/2 < 1 and state the largest integer that satisfies the inequality.

Learn how to solve the inequality -x/2 < 1 step-by-step. This problem covers algebraic concepts involving inequalities, including reversing inequality signs when dividing by a negative number. Suitable for students in Grades 7-9.

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