Question

solve the inequality and graph the solution.
n - 3 < 2
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.
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Explanation:

Step1: Isolate the variable n

To solve the inequality \( n - 3 < 2 \), we add 3 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the direction of the inequality remains the same.
So, \( n - 3 + 3 < 2 + 3 \)
Simplifying both sides, we get \( n < 5 \)

Step2: Graph the solution

For the inequality \( n < 5 \), we need to represent all real numbers less than 5 on the number line.

• First, we identify the endpoint, which is 5. Since the inequality is strict (\( < \), not \( \leq \)), we use an open circle at 5 to indicate that 5 is not included in the solution set.
• Then, we draw an arrow to the left of 5 to show that all numbers less than 5 are part of the solution.

Answer:

The solution to the inequality \( n - 3 < 2 \) is \( n < 5 \). To graph it, place an open circle at 5 on the number line and draw an arrow pointing to the left (towards numbers less than 5).