What is the solution set for 12−6x>24
?(1 point)
Responses
x>2
x is greater than 2
x<2
x<2
x>−2
x is greater than negative 2
x<−2
And can you explain how you got the answer?
To solve the inequality 12 − 6x > 24, we need to isolate the variable x.
First, we can start by subtracting 12 from both sides of the inequality:
12 - 6x - 12 > 24 - 12
This simplifies to:
-6x > 12
Next, we can divide both sides of the inequality by -6. However, when dividing or multiplying by a negative number, we need to flip the inequality sign.
-6x/ -6 < 12/ -6
This gives us:
x < -2
Therefore, the solution set for the inequality 12 − 6x > 24 is x < -2.
Why do we need to flip the inequality sign?
We need to flip the inequality sign when dividing or multiplying by a negative number in order to maintain the correct direction of the inequality.
When we divide both sides of an inequality by a positive number, the direction of the inequality remains the same. For example, if we have x > 2 and we divide both sides by a positive number, say 3, we get x/3 > 2/3. The inequality still holds true.
However, when we divide both sides of an inequality by a negative number, the direction of the inequality needs to be flipped. This is because dividing by a negative number switches the order of numbers on the number line. For example, if we have x < -2 and we divide both sides by -3, we get x/(-3) > (-2)/(-3), which simplifies to x/(-3) > 2/3. To maintain the same order on the number line, we need to flip the inequality sign, resulting in x < 2/3.