When I'm dealing with inequalities, I find it really important to understand how negative and positive numbers interact. First, I keep in mind that when I multiply or divide both sides of an inequality by a negative number, I need to flip the inequality sign. For example, if I have ( -2x > 4 ) and I divide both sides by -2, I must switch the sign, which gives me ( x < -2 ).
I also pay close attention to how the sign of the numbers affects the direction of the inequality. For example, if I have ( x + 3 < 5 ), I can easily see that ( x < 2 ) since both numbers are positive. However, when I'm dealing with negative numbers, it can get a bit trickier. For instance, if Iām comparing negative values, I have to remember that -1 is greater than -5, which can confuse me if Iām not careful.
Overall, when I work with inequalities, I make sure to keep track of the signs and remember to flip the inequality when necessary. It helps me solve problems accurately, especially when both negative and positive numbers are involved.