We want to write an inequality that compares the numbers 6 and - 3. To do so, we will mark both numbers on the same number line. Let's do it!
We can see that the number 6 is to the right from the number - 3. This means that 6 is greater than - 3. Let's write it as an inequality.
6 > - 3
Now, we want to determine whether the inequality remains true if we multiply each number by 2. Let's recall the Multiplication Property of Inequality.
Multiplication Property of Inequality (Case 1)
When we multiply each side of an inequality by the same positive number, the inequality remains true.
This means we can multiply each side of the inequality by 2 and it remains true. That is because 2 is a positive number. Let's check it by multiplying both sides of the inequality by 2.
6 * 2 ? > - 3 * 2 ⇒ 12 > - 6 ✓
Finally, we will check whether the inequality remains true if we multiply each number by - 2. Let's recall the second case of the Multiplication Property of Inequality.
Multiplication Property of Inequality (Case 2)
When we multiply each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed for the inequality to remains true.
This means that we have to reverse the inequality symbol while multiplying by - 2. That is because - 2 is a negative number. The inequality does not remain true if we just multiply each number by - 2. Let's check it by multiplying both sides of the inequality by - 2.
6 * (- 2) ? > - 3 * (- 2) ⇒ - 12> 6 *
