2p - 4p < _ -2

that is less than or equal to because I don't know how to make the symbol on my computer
Then I get -2p < _ -2
Divide both sides by -2 to get p > _ 1
Is that correct, that when you divide by a negative number the sign changes direction??

Because the answer book says p < _ 1

I agree with you ... p ≥ 1

... the direction changes if you multiply or divide by a negative quantity

alt-242 and alt-243 are ≥ and ≤

or on a Mac, the ≥ is obtained by pressing "option" >

btw, I agree with R_scott, the correct answer is p ≥ 1

Yes, you are correct in stating that when you divide an inequality by a negative number, the direction of the inequality sign changes. However, there seems to be a mistake in your steps.

Let's start with the given inequality: 2p - 4p < _ -2.

Since you mentioned that it should be less than or equal to, we can rewrite it as 2p - 4p ≤ -2.

Next, simplify the left side of the inequality: -2p ≤ -2.

Now, in order to solve for p, divide both sides of the inequality by -2. Remember that when dividing by a negative number, the direction of the inequality sign must be flipped.

By dividing both sides by -2, we get: p ≥ 1.

So, the correct solution to the inequality is p ≥ 1, meaning that p is greater than or equal to 1.

Therefore, the answer book is incorrect if it states that p < 1. The correct solution should be p ≥ 1.