Question

solve the inequality and graph the solution.
\\(\frac{n}{2} < 2\\)
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
submit

Explanation:

Step1: Multiply both sides by 2

To solve the inequality \(\frac{n}{2} < 2\), we multiply both sides by 2 to isolate \(n\). Multiplying both sides of an inequality by a positive number does not change the direction of the inequality sign. So we have:
\(2\times\frac{n}{2} < 2\times2\)

Step2: Simplify both sides

Simplifying the left - hand side, \(2\times\frac{n}{2}=n\), and the right - hand side, \(2\times2 = 4\). So the solution to the inequality is \(n < 4\).

For graphing the solution:

• We draw a number line.
• Since the inequality is \(n < 4\) (not \(n\leq4\)), we use an open circle at \(n = 4\) to indicate that 4 is not included in the solution set.
• Then we draw an arrow to the left of 4 to show all the numbers less than 4.

Answer:

The solution to the inequality \(\frac{n}{2}<2\) is \(n < 4\). The graph of the solution has an open circle at \(4\) and an arrow pointing to the left along the number line.