What is the key thing you have to remember when multiplying or dividing by a negative number in inequalities?
you must get a negative answer
you cannot multiply or divide by a negative
you must switch the direction of the sign
you cannot get a negative answer
The key thing to remember when multiplying or dividing by a negative number in inequalities is that you must switch the direction of the sign.
The key thing to remember when multiplying or dividing by a negative number in inequalities is that you must switch the direction of the sign.
The key thing to remember when multiplying or dividing by a negative number in inequalities is that you must switch the direction of the sign. This is because multiplying or dividing both sides of an inequality by a negative number changes the inequality's direction.
To understand why this is the case, let's consider an example. Suppose we have the inequality 2x < 6. If we divide both sides by -2, we get (-2)(2x) / -2 < 6 / -2, which simplifies to -x > -3. Notice that we switched the direction of the inequality from "<" to ">".
To see why this happens, imagine a number line. Positive numbers are to the right of zero, and negative numbers are to the left. Multiplying or dividing by a positive number preserves the direction of the inequality. However, multiplying or dividing by a negative number effectively multiplies or divides by -1, which reverses the number's position on the number line. This switch in position is why we need to switch the direction of the inequality.
In summary, when multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality must be switched.