Why Do You Switch The Inequality Sign

It is a good question though. Therefore VALUE OF BLUE POINT VALUE OF RED POINT.

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On both sides what was positive becomes negative and what was negative becomes positive.

Why do you switch the inequality sign. When should you flip the inequality. So you must flip the inequality sign as well. Youll earn badges for being active around the site.

This is because of this rule of inequalities. When you multiply both sides by a negative value you make the side that is greater have a bigger negative number. Anytime you multiply or divide both sides of the inequality you must flip or change the direction of the inequality sign.

Multiplying or dividing both sides of an equation by a negative number changes the inequality of the equation because it changes the sign of each side of the equation. This means that if you had a less than sign. But when its multiplied by a negative number x becomes greater than y.

Summarizing multiplying an inequality by a negative number is the same as reversing their order on the number line. X x y y x y 1 y 1 x. If a b then a b.

This is called the Additive Inverse. So let us swap them over and make sure the inequalities point correctly. Our summary above is actually a mathematical theorem.

You only change the inequality sign if you divide or multiply both sides by a negative number. Taking the log doesnt change which way an inequality points except in a special case well get to at the end of this answer. That is why the inequality sign was reversed.

If you multiply both sides by -2 you need to change the. Why do you flip an inequality sign. Were multiplying x by negative one on the left but since its inside absolute value signs the outcome is still positive and then were multiplying the right side by negative one and switching the inequality sign because we.

Maybe in the end he needs to solve for n so he must multiply by ln 23 both sides and - as you wrote - since its negative he must switch the inequality sign. In the following example notice how the sign becomes a sign when the inequality is divided by -2 -2x - 10 2 -2x - 10 10 2 10 -2x 12 x -6 Dividing by -2 required the flipping of the inequality sign. As you can see x is originally less than y.

Report 4 years ago. If instead of the inequality sign you are using a lesser or greater than sign however you will need to reverse it if you multiply both sides by the same negative number eg. So when you divide by log 09 you are dividing by a.

Were essentially multiplying by 1. Positive numbers are greater than zero and are denoted with a sign or no sign at all. Log 09 -0046 to 3dp.

Thats because smaller negative numbers are closer to 0 making them worth more. 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. Similarly why do you switch the inequality sign.

Do you flip the inequality sign when you divide by a positive. Whenever you multiply or divide an inequality by a negative number you must flip the inequality sign. Why do you switch inequality signs.

6 x 3 And that is the solution. That is if and are real numbers and then. The answer key said so but I think they placed it at the wrong line ur right abt the dividing thing.

Notice that this is because we can multiply both sides of 1 by x y 1 to get. Because we are multiplying by a negative number the inequalities change direction. Dividing by a negative number is the same as dividing by a positive number and then multiplying by 1.

Much like when you divide by a negative number the sign of the inequality must flip. Alex has more money than Billy and so Alex is ahead. Rep gems come when your posts are rated by other community members.

Once all values become negative that means that negatives are flipped from one side to the other or abolished if both sides were negative. 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. In this video I show you examples of each with lots of practiceFor fun b.

But to be neat it is better to have the smaller number on the left larger on the right. Which naturally flips the signs however if x y 1 is negative which occurs when x and y are different signs then we have to flip the inequality sign back because we multiplied by negative number. If a b then a b.

Much like when you divide by a negative number the sign of the inequality must flip. Flip the inequality sign when you multiply or divide both sides of an inequality by a negative number. The inequality sign changes because you are switching the signs of the values in the inequality.

But multiplying by 1 is the same as switching the signs of the numbers on both sides of the inequality which reverses the inequality. You must have remembered the rule that if you multiply both sides of an inequality by 1 you have to flip the sign of the inequality as well. Thus if you divide or multiply both sides by a positive numberthe inequality sign will not change.

We solve inequalities the same way we solve equations except that when we multiply or divide both sides of the inequality by a negative number we have to do something special to it. Anytime you multiply or divide both sides of the inequality you must flip or change the direction of the inequality sign. There are three times when you NEED to change flip or reverse an inequality sign.

This is really the same as multiplying by -1 and that is why it changes direction. You also often need to flip the inequality sign. Into a so -20-8.

As we just saw putting minuses in front of a and b changes the direction of the inequality. Log 09 is a negative number. When you divide or multiply by a negative number you must change the direction of the inequality sign.

Why do you have to flip the inequality sign.

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