Question

solve the inequality and graph the solution.
-6 + 5k ≥ 9
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
number line with -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
submit

Explanation:

Step1: Add 6 to both sides

To isolate the term with \( k \), we add 6 to both sides of the inequality \(-6 + 5k \geq 9\). This gives us \( -6 + 6+ 5k \geq 9 + 6 \), which simplifies to \( 5k \geq 15 \).

Step2: Divide by 5

Now, we divide both sides of the inequality \( 5k \geq 15 \) by 5. So, \( \frac{5k}{5} \geq \frac{15}{5} \), which simplifies to \( k \geq 3 \).

To graph the solution:

• The endpoint is at \( k = 3 \). Since the inequality is "greater than or equal to", the endpoint is a closed circle (filled in).
• The arrow points to the right (towards positive infinity) because we are looking for all values of \( k \) that are greater than or equal to 3.

Answer:

The solution to the inequality is \( k \geq 3 \). For the graph, plot a closed circle at \( 3 \) on the number line and draw an arrow to the right.