When an Inequality expression is multiplied (or divided) by a negative number then the Inequality sign is reversed.
Example : -9x < 18 : -x < 2 : x > -2........as both sides have been multiplied by -1.
Always.
Flip it around
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.
Yes, it is true.
Because when you fit in the variables, it wouldn't be true. therefore, you have to flip the inequality sign For example, 3 > 2 True 3(-2) > 2(-2) -6 > -4 False If you change the direction of the inequality symbol, in the same time that you multiply by a negative number, then you find a true statement. 3 > 2 True 3(-2) < 2(-2) -6 < -4 True This is because the greater the absolute value of a negative number, the lesser it is, while the opposite is true for a positive number. When you multiply by a negative, a very large number becomes very small, or the opposite.
Always.
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.
You need to change it to the opposite direction; e.g 5 > 1; multiply both sides by -2 it becomes -10 < -2
Yes.
Flip it around
When a side is multiplied or divided by a negative number.
u only reverse the sign when u multiply or divide by a NEGATIVE number...otherwise u don't change the direction
When the two sides of the inequality are multiplied or divided by a negative number or term or expression.
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.
When multiplying or dividing a negative number or variable.
The inequality symbol shows wich side of the equation is greater than the other. When you multiply a positive number by a negative number you get a negative result ( for instance 4 x -2 = -8 ). 4 is larger than -8. If we multiply a negative number by a negative number we get a positive number. 1) -5 > -6 . -1 (-5) < -1(-6) . 5 < 6 this is a true statement 2) 5 > -6 . -1 (5) < -1 (-6) . -5 < 6 this is also true 3) 6 > 5 . -1 (6) < -1 (5) . -6 < - 5 this one works too
"<" means "farther to the left on the number line " and ">" means "farther to the right on the number line". Multiplying by a negative number switches the sign, which is a reflection that turns left into right. Double switch example: 1<2 multiply this by (-2): -2>-4 multiply this by (-1): 2<4