I know when solving inequalities the sign changes when you multiply or divide by a negative number, my question is does this happen in equations as well?
No, it doesn't. The equal sign is symmetrical, so reversal is not possible.
4>2 implies -4<-2
4=2+2 implies -4 = -(2+2)
In equations, the sign does not change when you multiply or divide by a negative number. This is a key difference between inequalities and equations.
When you're solving equations, you are trying to find the values of the variable(s) that make the equation true. In equations, both sides of the equation are equal, so any operation you perform on one side of the equation must also be performed on the other side in order to maintain that equality.
Let's consider an example equation:
2x = 8
If you divide both sides of the equation by 2, you get:
(2x) / 2 = 8 / 2
x = 4
Notice that the sign (equal to) did not change during the division. This is because both sides of the equation were divided by the same positive number, 2.
So, unlike inequalities, where the sign changes when you multiply or divide by a negative number, in equations the sign remains the same regardless of whether you multiply or divide by a positive or negative number.