Question

which graph represents the solutions to this inequality? 8v - 15 ≥ -39 and 3v + 4 < 61

Explanation:

Step1: Solve the first inequality

Solve \(8v - 15\geq - 39\).
Add \(15\) to both sides: \(8v\geq - 39 + 15\), so \(8v\geq - 24\).
Divide both sides by \(8\): \(v\geq - 3\).

Step2: Solve the second inequality

Solve \(3v + 4\lt61\).
Subtract \(4\) from both sides: \(3v\lt61 - 4\), so \(3v\lt57\).
Divide both sides by \(3\): \(v\lt19\).

Step3: Combine the solutions

The solution of the compound - inequality \(v\geq - 3\) and \(v\lt19\) is \(-3\leq v\lt19\).
On a number - line, a closed circle at \(-3\) (because \(v = - 3\) is included in the solution set, due to \(\geq\)) and an open circle at \(19\) (because \(v = 19\) is not included in the solution set, due to \(\lt\)), with a line segment connecting them.

Answer:

The third graph (with a closed circle at \(-3\), an open circle at \(19\), and a line segment between them) represents the solutions to the inequality.