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I bet you're thinking of > and <, the "greater than" and the "less than" signs, and not the "inequality" thing-- the = sign with a / through it. Am I right? Think about the positive integers 3 and 5. It should be easy to see that 3 is smaller than 5. Now here's a trick. If you think about the number line, even if you go back and forth over the zero point, "smaller" is always to the left, and "greater" is always to the right.

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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9

<-------------- smaller larger --------------->

The weird thing is that when you're moving to the left and you cross zero, the numbers look like they're getting bigger-- except for the negative sign. You have to use your imagination with these negative integers. Say that you have 10 cd's. If I take two of them, I'm really adding "negative 2" to the total. This leaves you with 8 cd's. The "negative 2" made you total smaller, but not by much. I give back the two I took, and now I take 8 of them. I'm really adding "negative 8" to the 10 cd's. This leaves you with only two! So the "negative 8" had the effect of making your collection MUCH smaller than the "negative 2" did. So in a sense, the -8 is "smaller" than the -2. It fits with the number line, and the fact that numbers get smaller as you move to the left.

Now back to 3 and 5. Look at the number line. +3 < +5. three is smaller than 5. If I multiply them both by -1, I now have -3 and -5. If you look at the number line, you will see that -5 is to the left of -3! This means that

-3 > -5.

So to put it simply... when you multiply or divide a number with a negative number, the number becomes a negative number, therefore causing it to be smaller than the original number. Therefore the sign changes accordingly.

Q: Why does the inequality sign change when both sides are multilpied or divided by a negative number?

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When a side is multiplied or divided by a negative number.

The inequality symbol doesn't change direction in this case.Note that that is the same as adding a positive number.Note also that if you MULTIPLY or DIVIDE by a negative number, then you need to change the direction of the inequality symbol.

I cannot tell you why it changes however it does happen with an equation as most inequalities start off in an equation.

You need to change it to the opposite direction; e.g 5 > 1; multiply both sides by -2 it becomes -10 < -2

Most of the steps are the same. The main difference is that if you multiply or divide both sides of an inequality by a NEGATIVE number, you must change the direction of the inequality sign (for example, change "less than" to "greater than").

Related questions

It changes because the number may be lesser than the original equation. The greater the negative number the more likely the inequality sign will change.

When a side is multiplied or divided by a negative number.

When the two sides of the inequality are multiplied or divided by a negative number or term or expression.

The sign changes if you multiply/divide by a negative number. It stays the same if you add/subtract by a negative number.

It's the same thing as solving an equation, the minor difference is to change the inequality sign when the numbers change signs(i.e negative to positive to negative).

The inequality symbol doesn't change direction in this case.Note that that is the same as adding a positive number.Note also that if you MULTIPLY or DIVIDE by a negative number, then you need to change the direction of the inequality symbol.

-x > a iff** x < -a This is easy to see intuitively by coloring a number line. ** "if and only if"

Yes you have to flip the sign.

You divide as normal BUT you change the direction of the inequality symbol, so that < becomes > and conversely.

No. Only when you divide by a negative.

I cannot tell you why it changes however it does happen with an equation as most inequalities start off in an equation.

yes it does