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The inequality given is:

\[
\frac{5}{2} > -\frac{x}{4}
\]

Let's solve for \(x\).

1. First, eliminate the fraction by multiplying both sides of the inequality by 4 (the denominator of \(\frac{x}{4}\)):

\[
4 \times \frac{5}{2} > 4 \times -\frac{x}{4}
\]

This simplifies to:

\[
10 > -x
\]

2. Now, solve for \(x\) by multiplying both sides by -1. Remember, when multiplying or dividing by a negative number, the inequality sign reverses:

\[
-10 < x
\]

Thus, the solution is:

\[
x > -10
\]

Would you like any further details or have questions? Here are some related practice questions:

1. Solve \( \frac{3}{2} > -\frac{x}{5} \) for \(x\).
2. Solve the inequality \( \frac{7}{3} > -\frac{y}{6} \).
3. Solve for \(x\) in \( \frac{6}{4} > -\frac{x}{7} \).
4. How does multiplying or dividing an inequality by a negative number affect the inequality?
5. What is the difference between solving inequalities and solving equalities?

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

Learn how to solve the inequality 5/2 > -x/4 with a step-by-step solution. This problem involves multiplying both sides by 4 and reversing the inequality when dividing by a negative number. Suitable for Grades 7-9 students working on algebraic inequalities.

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