Question

What property of inequality justifies the steps shown in the following solution process?

4/3d≥−20

3/4(4/3)d≥−20(3/4)

d≥−15

(1 point)

Answer 1

The property of inequality that justifies the steps shown in the solution process is the **Multiplication Property of Inequalities**.

According to this property, when you multiply both sides of an inequality by a positive number, the inequality remains unchanged. In this case, multiplying both sides of the inequality \(4/3d \geq -20\) by \(3/4\) (which is a positive number) results in:

\[
\frac{3}{4} \left( \frac{4}{3}d \right) \geq -20 \left( \frac{3}{4} \right)
\]

This leads to:

\[
d \geq -15
\]

So, the reason this step is valid is due to the **Multiplication Property of Inequalities**.