Question

solve for n and graph the solution. -3 - 2n ≤ -4n + 13 < 5 - 2n put the endpoints. select an endpoint to change it from closed to open. select a segment, ray, or line to delete it.

Explanation:

Step1: Solve the left - hand inequality

Solve \(-3 - 2n\leqslant-4n + 13\).
Add \(4n\) to both sides: \(-3 - 2n+4n\leqslant-4n + 13+4n\), which simplifies to \(-3 + 2n\leqslant13\).
Add \(3\) to both sides: \(-3+3 + 2n\leqslant13 + 3\), so \(2n\leqslant16\).
Divide both sides by \(2\): \(n\leqslant8\).

Step2: Solve the right - hand inequality

Solve \(-4n + 13\lt5 - 2n\).
Add \(4n\) to both sides: \(-4n+4n + 13\lt5 - 2n+4n\), which simplifies to \(13\lt5 + 2n\).
Subtract \(5\) from both sides: \(13 - 5\lt5 - 5+2n\), so \(8\lt2n\).
Divide both sides by \(2\): \(4\lt n\).

Answer:

The solution of the compound inequality is \(4\lt n\leqslant8\). On the number - line, we have an open circle at \(n = 4\) (because \(n\gt4\)) and a closed circle at \(n = 8\) (because \(n\leqslant8\)) and the line segment connecting these two points.