Question

which graph represents the solutions to this inequality? 3a - 11 ≥ 16 and 2a - 8 < 22

Explanation:

Step1: Solve the first inequality

Solve \(3a - 11\geq16\). Add 11 to both sides: \(3a- 11 + 11\geq16 + 11\), which simplifies to \(3a\geq27\). Then divide both sides by 3: \(a\geq9\).

Step2: Solve the second inequality

Solve \(2a - 8<22\). Add 8 to both sides: \(2a-8 + 8<22 + 8\), which simplifies to \(2a<30\). Then divide both sides by 2: \(a < 15\).

Step3: Determine the solution set

The solution of the compound - inequality is \(9\leq a<15\). On a number line, this is represented by a closed circle at 9 (because \(a\) can equal 9) and an open circle at 15 (because \(a\) cannot equal 15) with a line segment connecting them.

Answer:

The graph with a closed circle at 9 and an open circle at 15 and a line segment between them.