Given: −3(a–b)<0, which is the greater: a or b? Give numerical examples.
since -3 is negative, the other factor must be positive
So, a > b
-3(a-b) < 0.
divide both sides by -3 and reverse the inequality sign:
a - b > 0.
a > b.
To determine which is greater between a and b, we need to examine the inequality −3(a–b)<0.
To solve this inequality, we should isolate the variable by dividing both sides by −3. But since we're dividing by a negative number, we need to flip the inequality sign.
Dividing by −3, we have:
(a–b) > 0
Now, we can further simplify the inequality by expanding the parentheses.
a - b > 0
From this, we can see that a is greater than b for this inequality to hold. In other words, the value of a is greater than the value of b.
To illustrate this with numerical examples, let's assume a = 5 and b = 3. We substitute these values into the inequality:
5 - 3 > 0
2 > 0
Since 2 is indeed greater than 0, this example supports our statement that a is greater than b.
Let's try another example with a different set of numbers: a = 2 and b = 4.
2 - 4 > 0
-2 > 0
In this case, -2 is not greater than 0, which contradicts our statement that a should be greater than b. Therefore, this example does not support our conclusion.
Hence, through the inequality −3(a–b)<0, we have determined that a is greater than b.