Question

you found that -9 is the boundary point and is also a solution to the inequality. how can you represent this on a number line?
$d - 5 \geq - 14$
$d - 5 = - 14$
$d = - 9$

Explanation:

Step1: Understand the rule for boundary points in inequalities

If the boundary point is a solution (i.e., the inequality is $\geq$ or $\leq$), we use a closed - circle (filled - in circle) on the number line. If the boundary point is not a solution (i.e., the inequality is $>$ or $<$), we use an open - circle (unfilled circle).

Step2: Analyze the given inequality

The given inequality is \(d - 5\geq - 14\). The boundary point is found by solving the equation \(d-5=-14\), which gives \(d = - 9\). Since the inequality is \(\geq\) (the boundary point \(d=-9\) is a solution).

Answer:

We use a closed - circle (filled - in circle) at \(-9\) on the number line to represent that \(-9\) is a solution to the inequality \(d - 5\geq - 14\).