Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not?
Numbers are organized with negative numbers valued less than zero (n<0), while positive numbers are valued more than zero (n>0).
In other terms:
X > 0
-X < 0
It does not happen with equations, because they are "equal" rather than "greater than" or "less than."
I hope this helps. Thanks for asking.
Because when you multiply or divide any number (a positive or a negative number) by a negative number you will automatically change the sign of the number you are performing the operation on. In an inequality you will then reverse the relationship between the numbers on each side of the inequality. Use some examples like: 2 less than 3 divided by -1 and you will see that the answer is -2 is greater than -3.
The equality of an equation is never changed if you perform the same operation on each side of the equation. Example: 2 + 2 = 4. If you add, subtract, multiply or divide each side of the equation by the same number the result will be an equality. Keep in mind that addition and multiplication are the only operations and that subtraction and division are only reverse addition and multiplication.
I am still getting confused when trying to solve.
no
The inequality sign changes when both sides are multiplied or divided by a negative number because multiplying or dividing by a negative number effectively reverses the inequality.
To understand why this happens, let's consider an example using the inequality 5 > 2. If we multiply both sides of the inequality by -1, we get -5 < -2. The original relationship between 5 and 2 has been reversed. This is because when we multiply both sides by -1, we are essentially multiplying both sides by a negative factor (-1 in this case), which changes the direction of the inequality.
The same principle applies when dividing both sides by a negative number. For instance, if we have -3 < -6 and we divide both sides by -2, we get 3 > 6. Again, the original relationship between -3 and -6 has been reversed.
It's important to note that this rule only applies to inequalities, not equations. In equations, both sides are considered equal, so multiplying or dividing by a negative number does not change the equality. For example, if we have 2 = 4, and we multiply both sides by -1, we still have -2 = -4, not -2 = 4.
In summary, the inequality sign changes when both sides are multiplied or divided by a negative number because the negative factor reverses the direction of the inequality, effectively swapping the relation between the two sides. However, this does not happen with equations, as the equality is not affected by multiplying or dividing by a negative number.