Hmm,,, let us see if I can answer this. I have two numbers 6 and 2 We know that 6> 2 on the number line Let us first multiply it with a positive number on either side When I multiply +6 on both sides, I get 6(+6) > 2(+6) 36 > 12 which is also true So, there is no need to flip the inequality in the middle. When I multiply with -6 on both sides without flipping the inequality in the middle, I get 6(-6) > 2(-6) or -36 > -12. Is this true? No, -36 \ngtr -12 because as we move down the number line, as the negative number increases its value decreases. So this means that when I multiply with a negative number, the inequality will have to change So we make it a point to flip the inequality when we multiply this with a negative number Look at 6> 2 again This time I multiply with -6 on either side, and I also flip the inequality 6(-6)< 2(-6) -36 < -12 This is true.