Question

the rule that states \if you do something to one side of the equation, you must do it to the other side\ is known as the ______ of equality.

an equation that results in a false statement like 5=-3 after simplification has ______ solutions.

the type of solution where there is exactly one value that satisfies the equation is called ______.

the process of finding the value of variables that satisfy an equation is known as ______.

Explanation:

First Question:

The rule described is a fundamental principle in solving equations, where to maintain equality, operations on one side must be mirrored on the other. This is the "property of equality" (specifically, the addition, subtraction, multiplication, or division property, but generally referred to as the property of equality).

When an equation simplifies to a false statement (like \(5 = -3\)), it means no value of the variable can satisfy the equation, so it has no solutions.

An equation with exactly one value that makes it true is said to have a unique solution, often called a "one - solution" or "unique solution" case. The term for this type of solution is "unique solution" (or "one solution").

Answer:

property

Second Question: