Question

solve the inequality below, then choose the correct graph that represents the answer. 2n + 7 ≥ 27 or 3 + 3n ≤ 30

Explanation:

Step1: Solve \(2n + 7\geq27\)

Subtract \(7\) from both sides: \(2n\geq27 - 7\), so \(2n\geq20\).
Divide both sides by \(2\): \(n\geq10\).

Step2: Solve \(3+3n\leq30\)

Subtract \(3\) from both sides: \(3n\leq30 - 3\), so \(3n\leq27\).
Divide both sides by \(3\): \(n\leq9\).

The solution of the compound inequality \(2n + 7\geq27\) or \(3 + 3n\leq30\) is \(n\leq9\) or \(n\geq10\).

On a number - line, for \(n\leq9\), we have a closed circle at \(9\) (since the inequality is \(\leq\)) and the line extends to the left. For \(n\geq10\), we have a closed circle at \(10\) (since the inequality is \(\geq\)) and the line extends to the right.

Answer:

The first option (the number - line with closed circles at \(9\) and \(10\) and the line extending to the left from \(9\) and to the right from \(10\)) is the correct graph.