Question

solve the inequality and graph the solution.
-8 + 6n < 4
plot the endpoints. select an endpoint to change it from close middle of the segment, ray, or line to delete it.

Explanation:

Step1: Isolate the term with the variable

Add \(8\) to both sides of the inequality \(-8 + 6n<4\).
Using the addition property of inequalities: \(-8+8 + 6n<4 + 8\), which simplifies to \(6n<12\).

Step2: Solve for \(n\)

Divide both sides of the inequality \(6n<12\) by \(6\).
Using the division property of inequalities: \(\frac{6n}{6}<\frac{12}{6}\), so \(n < 2\).

To graph the solution \(n < 2\) on a number - line:

• The endpoint is at \(n = 2\). Since the inequality is strict (\(<\)), we use an open circle at \(n = 2\).
• The solution set includes all numbers less than \(2\), so we draw a ray to the left of \(2\) on the number - line.

Answer:

The solution of the inequality \(-8 + 6n<4\) is \(n < 2\). On the number - line, we have an open circle at \(2\) and a ray extending to the left.