Inequalities when do you flip the sign

It's called flipping the inequality sign. Let's see what exactly this looks like. We can use our inverse property of addition subtracting 4 from both sides. But there's a faster way. In words, the variable x is greater than or equal to Notice how the sign of the inequality flipped when we multiplied by negative one.

Much like when you divide by a negative number, the sign of the inequality must flip! Here's why:. Imagine comparing the numbers 5 and 3. Obviously this is wrong! When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side!

This is why you must flip the sign whenever you multiply by a negative number. You can also consider this with a number line.

On a number line, 5 is to the right of 3. I have a step-by-step course for that. Learn More. Solving inequalities by clearing the negative values Example Solve the inequality. Example Solve the inequality. Get access to the complete Algebra 1 course.

Get started. Learn math Krista King November 30, math , learn online , online course , online math , algebra , algebra 1 , algebra i , inequalities , negative numbers , multiplying by a negative , dividing by a negative , inequality. You also need to think about flipping the inequality sign when you're dealing with absolute value problems. Then first of all you want to isolate the absolute value expression on the left side of the inequality it makes life easier.

Subtract 6 from both sides to get:. Now, you need to rewrite this expression as a compound inequality. The output of an absolute value expression is always positive, but the " x " inside the absolute value signs might be negative, so we need to consider the case when x is negative. That gives us our two inequalities or our "compound inequality".

We can easily solve both of them. These kinds of problems take some practice, so don't worry if you aren't getting it at first! Keep at it and it will eventually become second nature. You also often need to flip the inequality sign when solving inequalities with absolute values. How to Divide Negative Fractions. How to Solve Double Inequalities.