Question

1. $n geq -\frac{2}{3}; -\frac{4}{9}$

Explanation:

Step1: Convert to common denominator

To compare $-\frac{2}{3}$ and $-\frac{4}{9}$, find a common denominator. The least common denominator of 3 and 9 is 9. So, $-\frac{2}{3}=-\frac{2\times3}{3\times3}=-\frac{6}{9}$.

Step2: Compare the two fractions

Now we have $-\frac{6}{9}$ (equivalent to $-\frac{2}{3}$) and $-\frac{4}{9}$. For negative fractions, the one with the larger numerator (in absolute value) is smaller. Since $|-6| = 6$ and $|-4| = 4$, and $6>4$, we have $-\frac{6}{9}<-\frac{4}{9}$, which means $-\frac{2}{3}<-\frac{4}{9}$.

Step3: Check the inequality

The inequality is $n\geq-\frac{2}{3}$. We need to check if $-\frac{4}{9}$ satisfies this. Since $-\frac{4}{9}>-\frac{2}{3}$ (from Step 2), $-\frac{4}{9}$ is greater than $-\frac{2}{3}$, so it satisfies $n\geq-\frac{2}{3}$.

Answer:

$-\frac{4}{9}$ satisfies the inequality $n\geq-\frac{2}{3}$ because $-\frac{4}{9}>-\frac{2}{3}$.