Subjects algebra

Inequality N Values Ee2E5F

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We need to find all values of $n$ from the given list that satisfy the inequality $$\frac{1}{3}n > \frac{2}{5}.$$ 2. **Write the inequality and isolate $n$:** Multiply both sides by 3 to eliminate the denominator on the left side. Since 3 is positive, the inequality direction stays the same. $$\cancel{3} \times \frac{1}{3} n > \cancel{3} \times \frac{2}{5}$$ $$n > \frac{6}{5}.$$ 3. **Interpret the inequality:** We want all $n$ values greater than $\frac{6}{5} = 1.2$. 4. **Check each candidate value:** - $\frac{3}{4} = 0.75$ (not greater than 1.2) - $\frac{6}{5} = 1.2$ (not greater than 1.2, equal) - $\frac{4}{3} \approx 1.333$ (greater than 1.2) - $1$ (not greater than 1.2) - $2$ (greater than 1.2) 5. **Conclusion:** The values that satisfy the inequality are $\frac{4}{3}$ and $2$.