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

Answer 1

What property of inequality can justify the math in Step 2?

Step 2:

−18w+42−42>−66−42

−18w>−108

Answer 2

The property that justifies these steps is the multiplication property of inequality. According to this property, if you multiply both sides of an inequality by a positive number, the direction of the inequality remains the same. In this case, multiplying both sides of the inequality by 3/4 maintains the direction of the inequality.

Answer 3

The property that justifies Step 2 is the addition property of inequality. According to this property, if you subtract the same number from both sides of an inequality, the direction of the inequality remains the same. In this case, subtracting 42 from both sides of the inequality maintains the direction of the inequality.