Question

graph the solution to the inequality on the number line.
$|4v + 12|\geq4$

Explanation:

Step1: Solve the inequality \(|4v + 12|\geq4\)

We know that if \(|x|\geq a\) (\(a\geq0\)), then \(x\geq a\) or \(x\leq - a\).
For \(|4v + 12|\geq4\), we have two cases:
Case 1: \(4v+12\geq4\)
Subtract 12 from both sides: \(4v\geq4 - 12\), so \(4v\geq - 8\).
Divide both sides by 4: \(v\geq - 2\).
Case 2: \(4v + 12\leq-4\)
Subtract 12 from both sides: \(4v\leq-4 - 12\), so \(4v\leq-16\).
Divide both sides by 4: \(v\leq - 4\).

Step2: Graph the solution on the number line

For \(v\geq - 2\), we draw a closed circle at \(v=-2\) (because the inequality is \(\geq\)) and shade to the right.
For \(v\leq - 4\), we draw a closed circle at \(v = - 4\) (because the inequality is \(\leq\)) and shade to the left.

Answer:

The solution of the inequality \(|4v + 12|\geq4\) is \(v\leq - 4\) or \(v\geq - 2\). On the number - line, we have a closed circle at \(v=-4\) with shading to the left and a closed circle at \(v = - 2\) with shading to the right.