Question

which graph represents the solution to ( v + 4 geq 2 ) and ( 8v - 20 leq 36 )?

Explanation:

Step1: Solve the first inequality

Solve \(v + 4\geq2\). Subtract 4 from both sides: \(v\geq2 - 4\), so \(v\geq - 2\).

Step2: Solve the second inequality

Solve \(8v-20\leq36\). Add 20 to both sides: \(8v\leq36 + 20\), then \(8v\leq56\). Divide both sides by 8: \(v\leq7\).

The solution of the compound - inequality \(v + 4\geq2\) and \(8v-20\leq36\) is \(-2\leq v\leq7\). On a number - line, this is represented by a solid circle at \(-2\) (because \(v=-2\) is included in the solution set, since the inequality is \(\geq\)) and a solid circle at \(7\) (because \(v = 7\) is included in the solution set, since the inequality is \(\leq\)) with a line segment connecting them.

Answer:

The third option (the number - line with a solid circle at \(-2\) and a solid circle at \(7\) and a line segment between them) is the correct graph.