Question

solve the inequality and graph the solution.
( 1 leq \frac{n + 4}{6} )
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.
←
-5 -4 -3 -2 -1 0 1 2 3 4 5
→
submit

Explanation:

Step1: Multiply both sides by 6

To eliminate the denominator, we multiply both sides of the inequality \(1 \leq \frac{n + 4}{6}\) by 6. This gives us \(1\times6 \leq \frac{n + 4}{6}\times6\), which simplifies to \(6 \leq n + 4\).

Step2: Subtract 4 from both sides

Now, we subtract 4 from both sides of the inequality \(6 \leq n + 4\) to solve for \(n\). So, \(6 - 4 \leq n + 4 - 4\), which simplifies to \(2 \leq n\) or \(n \geq 2\).

To graph the solution:

• The endpoint is at \(n = 2\). 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 \(n\) that are greater than or equal to 2.

Answer:

The solution to the inequality is \(n \geq 2\). For the graph, plot a closed circle at \(2\) on the number line and draw an arrow to the right.