What happens to the signs in an inequality when you multiply or divide on both sides by a negative?
What happens to the signs in an inequality when you multiply or divide on both sides by a negative?
The same thing that happens in an equation.
I hope this helps. Thanks for asking.
...however the "inequality sign" has to be reversed.
e.g.
-3x > 15
x < -5
When you multiply or divide both sides of an inequality by a negative number, the signs of the inequality reverse.
To understand why this happens, let's consider the following inequality:
a < b
If you multiply both sides by a positive number, say c, the inequality remains the same:
c * a < c * b
However, if you multiply both sides by a negative number, say -c, the inequality changes:
(-c) * a > (-c) * b
In this case, the less than sign (<) becomes a greater than sign (>) and vice versa.
The reason for this reversal lies in the properties of negative numbers. When you multiply or divide both sides of an inequality by a negative number, you are effectively multiplying or dividing by a number less than zero. Since multiplying or dividing by a negative number changes the sign, the direction of the inequality must also change to maintain the relationship between the numbers.