Asked by naw
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?
?(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?
Answers
Answered by
naw
Why do we need to flip the inequality sign?
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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.
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.