Question

solve the inequality and graph the solution.
-2 > 4n + 6
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.

<--(-5)---(-4)---(-3)---(-2)---(-1)---(0)---(1)---(2)---(3)---(4)---(5)--->

Explanation:

Step1: Subtract 6 from both sides

To isolate the term with \( n \), we subtract 6 from both sides of the inequality \( -2 > 4n + 6 \). This gives us \( -2 - 6 > 4n + 6 - 6 \), which simplifies to \( -8 > 4n \).

Step2: Divide both sides by 4

Next, we divide both sides of the inequality \( -8 > 4n \) by 4 to solve for \( n \). So, \( \frac{-8}{4} > \frac{4n}{4} \), which simplifies to \( -2 > n \) or equivalently \( n < -2 \).

Answer:

The solution to the inequality is \( n < -2 \). To graph this, we place an open circle at \( -2 \) (since the inequality is strict, \( n \) cannot equal \( -2 \)) and draw a ray to the left of \( -2 \) on the number line.