Just think about it--say you had two numbers....5 and 7. 7 is greater than five, obviously. But if you divide both numbers by -1, you get -5 and -7. -7 is less than -5.
Basically, with positive numbers, the farthest the number is from zero (the bigger its absolute value) the greater it is. But with negatives, the closest it is to zero (or the smallest its absolute value) the greater it is. So if you divide by -1 the absolute value stays the same while the sign changes, as does the relation between the two numbers.
The same applies when one number is negative and the other positive, or if your dividing by a number greater than one or less than one. Dividing by a negative always changes the sign.
Hope this helps/
yes it does
-x > a iff** x < -a This is easy to see intuitively by coloring a number line. ** "if and only if"
The sign changes if you multiply/divide by a negative number. It stays the same if you add/subtract by a negative number.
Yes, when you divide or multiply an inequality by a negative number, you must reverse the inequality sign. For example, if ( a < b ) and you multiply both sides by a negative number ( -c ), the inequality becomes ( -ac > -bc ). This change is necessary to maintain the truth of the inequality.
No. Only when you divide by a negative.
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.
yes it does
-x > a iff** x < -a This is easy to see intuitively by coloring a number line. ** "if and only if"
I cannot tell you why it changes however it does happen with an equation as most inequalities start off in an equation.
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.
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).
no because if the same is added to both sides they stay inequal example: 4≠6 (*5) 20≠30
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.
Yes you have to flip the sign.
Yes, when you divide or multiply an inequality by a negative number, you must reverse the inequality sign. For example, if ( a < b ) and you multiply both sides by a negative number ( -c ), the inequality becomes ( -ac > -bc ). This change is necessary to maintain the truth of the inequality.