Use two arbitrary numbers represented by the letters A and B. Now divide the question into a few cases.
Case 1. A < B and both are positive. Take any A and B and put them on your number line. Now look at the opposite of B which is -B and notice it will be farther to the left than -A which is the opposite of A. So we have -B<-A which we can written as -A>-B.
So for the first case, we see why we reverse the inequality symbol.
Case 2. Now look at A<B where both are negative. The exact same thing that happens in case 1 above, happens in this case. Try two number, say -2 and -1.
Case 3. Now say A is negative and B is positive. The other way around is the same thing. So Since A is negative, its opposite is positive and the opposite of B is negative. Any negative number is smaller than a positive number. So once again, we reverse the inequality symbol.
Try all three of these cases with some positive and negative number and a number line and you will see how this works, then generalize to A and B where they are arbitrary numbers. This is the way mathematician often prove things. They first use numbers and then generalize.
When one side of the inequality is divided or multiplied by a negative number.
When multiplying or dividing a negative number or variable.
In the case of an inequality, if you mulitply by a negative number, you have to reverse the direction of the inequality. E.g.: -x < 10 becomes: x > -10 (Here, I multiplied by -1, and simultaneously reversed the direction of the inequality.)
"<" 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
The inequality is "flipped" when multiplied by a negative number. For example, if x > y and a is a negative number, then ax < ay.
When one side of the inequality is divided or multiplied by a negative number.
No. Only flip the inequality when multiplying or dividing by a negative number.
You need to reverse the inequality symbol when multiplying both sides of an inequality by a negative number because you are changing the sign of both sides of the equation. Since inequality, such as "less than", means "to the left of" on the number line (where left is minus and right is plus) then a number that is less than another will be greater than the other if the signs were reversed. Example: 3 is less than 4, but -3 is greater than -4.
When multiplying or dividing a negative number or variable.
Yes, it is true.
When an inequality is multiplied or divided by a negative number the inequality sign is reversed.Example : -x < 7 ......after multiplying by (say) -2 this becomes 2x > -14
In the case of an inequality, if you mulitply by a negative number, you have to reverse the direction of the inequality. E.g.: -x < 10 becomes: x > -10 (Here, I multiplied by -1, and simultaneously reversed the direction of the inequality.)
Because your multiping the inverse to both sides
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.
When you multiply both sides by a negative number the inequality must be flipped over. You do not do that when multiplying by a positive number.
Flip. You need to reverse the inequality when multiplying or dividing by a negative. -2x < 10 (-1)*(-2x) < (-1)*10 2x > -10 x > -5
It changes the direction of the inequality.