Answer:
The correct answer is B. When you multiply or divide the inequality by a negative number, you must flip the inequality sign.
Explanation:
When solving inequalities, it's crucial to consider the impact of multiplying or dividing both sides of the inequality by a negative number. The reason behind this is rooted in the properties of inequalities and how they relate to the concept of negative numbers.
Let's start with an example inequality:
⇒ x > 3
This inequality indicates that the value of "x" is greater than 3. Now, suppose you multiply both sides of the inequality by -1. The result would be:
⇒ -x > -3
Here's where the difference comes into play, since you multiplied both sides by -1 (which is a negative number), you need to reverse the inequality sign. In this case, the greater-than sign (>) flips to a less-than sign (<), indicating that the value of -x is now less than -3. So we would have:
⇒ -x < -3
By reversing the inequality sign, we maintain the correct relationship between the values on both sides of the inequality.
To summarize, when multiplying or dividing both sides of an inequality by a negative number, it is essential to flip the inequality sign to maintain the inequality's validity. This is a key difference to remember when solving inequalities compared to equations, where the equality sign remains unchanged when manipulating the equation.
Let me also address the inequality you attached to the question. We have:
⇒ -3x + 2 < 8
As we would do with equations, our goal is to isolate the variable. Start by subtracting each side of the inequality by 2.
⇒ -3x < 8 - 2
⇒ -3x < 6
Now dividing each side of the equation by -3. Remember to flip the inequality.
⇒ x < 6/-3
∴ x > -2
Thus, the given inequality is solved.