Answer: To solve the inequality, we can start by isolating the variable k by subtracting 1 and 1/10 from both sides:
$-\frac{1}{10} + k \ge \frac{2}{5} - 1$
Simplifying, we get:
$k \ge \frac{2}{5} - \frac{5}{10} = \frac{2}{5} - \frac{1}{2}$
$k \ge \frac{4}{10} - \frac{5}{10} = -\frac{1}{10}$
So the solution to the inequality is:
$k \ge -\frac{1}{10}$
To graph this solution on a number line, we would start by drawing a line and marking a point at $-\frac{1}{10}$. Then, since the inequality includes the endpoint $-\frac{1}{10}$ (i.e., $k$ can be equal to $-\frac{1}{10}$), we would draw a closed circle at that point. Finally, we would shade to the right of the circle, since all values of $k$ greater than or equal to $-\frac{1}{10}$ satisfy the inequality.
So the graph of the solution on the number line would look like this:
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-1/10
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We used the property of subtracting the same value from both sides of an inequality to isolate the variable and solve the inequality.
Explanation: