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For the same reason you must flip it when you multiply by a negative number. An example should suffice.
2 < 3
If you multiply by -1, without switching the sign, you get:
-2 < -3,
which is wrong. Actually,
-2 > -3.
Look at a number line if you are not sure about this - numbers to the left are less than numbers further to the right.
Dividing by a negative number is the same as multiplying by the reciprocal, which in this case is also negative.
These signs are strictly the "Greater than" and "Less than" signs. The inequality sign is an = with a / stroke through it. If you divide an inequality by -1 it remains an inequality.
What else can I help you with?
When you divide both sides of any inequality by a negative number you need to what the inequality symbol?
Flip it around
How do you divide by a negative in an inequality?
You divide as normal BUT you change the direction of the inequality symbol, so that < becomes > and conversely.
If you multiply an inequality by a negative number when should you reverse the inequality symbol?
Always.
When you divide both sides of an inequality by a negative number you need to blank the inequality symbol?
Flip. You need to reverse the inequality when multiplying or dividing by a negative. -2x < 10 (-1)*(-2x) < (-1)*10 2x > -10 x > -5
Is it true When dividing by a negative number the direction of the inequality symbol MUST be reversed?
Yes, it is true.
When you divide both sides of any inequality by a negative number you need to what the inequality symbol?
Flip it around
What happens to the inequality symbol when you subtract 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.
How do you divide by a negative in an inequality?
You divide as normal BUT you change the direction of the inequality symbol, so that < becomes > and conversely.
If you multiply an inequality by a negative number when should you reverse the inequality symbol?
Always.
When you divide both sides of an inequality by a negative number you need to blank the inequality symbol?
Flip. You need to reverse the inequality when multiplying or dividing by a negative. -2x < 10 (-1)*(-2x) < (-1)*10 2x > -10 x > -5
Does positive number become negative when it crosses the inequality symbol?
Yes.
When do you change the direction of an inequality symbol?
When a side is multiplied or divided by a negative number.
How do you know when to reverse the direction of an inequality symbol?
u only reverse the sign when u multiply or divide by a NEGATIVE number...otherwise u don't change the direction
When solving an inequality when is it necessary to change the direction of the inequality symbol?
When the two sides of the inequality are multiplied or divided by a negative number or term or expression.
Why do we flip the inequality symbol when multiplying or dividing by a negative number.?
We flip the inequality symbol when multiplying or dividing by a negative number because it preserves the logical relationship between the quantities involved. For example, if ( a < b ) and we multiply both sides by a negative number, the direction of their relationship changes; thus, ( -a > -b ). This is due to the nature of the number line, where multiplying or dividing by a negative number reverses the order of the numbers. Therefore, flipping the symbol ensures that the inequality remains true.
When do you reverse the inequality symbol in a two-step inequality?
When multiplying or dividing a negative number or variable.
Is it true When dividing by a negative number the direction of the inequality symbol MUST be reversed?
Yes, it is true.
